Simplify \(\sqrt{40}+\sqrt{160}\). [2]

(a) Write 230000 in standard form. [1]

(b) Work out \((4.2\times10^{32})-(4.2\times10^{31})\), giving your answer in standard form. [2]

(c) Work out \((80\times10^{50})^{1/3}\), giving your answer in standard form. [2]

(a) Simplify \((27x^9)^{-2/3}\). [3]

(b) Solve \(7^x=49^{1-2x}\). [3]

Find \(143^0\). [1]

\(710000.03=(7.1\times10^a)+(3\times10^b)\). Find \(a\) and \(b\). [2]

Evaluate \(27^{-\frac23}\times(6^4)^{0.5}\). [4]

Find \(x\) if \(7^{2x+1}=49^{2-x}\). [3]

(a) Expand and simplify \((5+\sqrt2)(3-\sqrt8)\). [3]

(b) \(\sqrt{2\frac9{20}}+\frac6{\sqrt5}=k\sqrt5\). Find \(k\). [4]

(a) Expand and simplify \((4-\sqrt7)(3+2\sqrt7)\). [2]

(b) Rationalise the denominator and simplify \(\frac2{3-\sqrt5}\). [3]

(a) Simplify \((\sqrt{0.1})^2\). [1]

(b) Rationalise \(\frac4{2-\sqrt2}\), giving the result in its simplest form. [3]

(a(i)) Simplify \((10b^4)^{-3}\). [2]

(a(ii)) Simplify \((8p^{15})^{\frac23}\). [2]

(b) Find n if \(16^n=64\). [2]

(a) Write \(7.83\times10^{-2}\) as an ordinary number. [1]

(b) Evaluate \((5.5\times10^6)(2\times10^{-3})\), giving the answer in standard form. [2]

Find the positive value of x when \(x^{-1/3}=16x^{-1}\). [3]

(a) Calculate \(\frac1{0.025^2}\). [1]

(b) Calculate \(\sqrt[4]{410+4^{-2}}\). [1]

(a) Simplify \(\sqrt{300}+\sqrt{48}\). [2]

(b) Rationalise and simplify \(\frac9{2+\sqrt7}\). [3]

(a) Simplify \(\left(\frac{x^2}{4}\right)^{3/2}\). [2]

(b) \(16^x\left(\frac12\right)^x=4^{x+3}\). Find x. [4]

(a) Write \(0.00709\) in standard form. [1]

(b) Work out \((4\times10^4)^2\) in standard form. [2]

Find \(27^{-2/3}\). [2]

(a) Expand and simplify \((2-\sqrt5)(1-3\sqrt5)\). [2]

(b) Rationalise \(6/\sqrt{10}\), giving the simplest form. [2]

(a) Write 0.00708 in standard form. [1]

(b) Work out \((3.8\times10^{22})+(3.8\times10^{23})\), giving standard form. [2]

(a) Find \(125^{2/3}\). [2]

(b) Find \(4^{-5/2}\). [2]

(a) Rationalise \(9/\sqrt3\), giving the simplest form. [2]

(b) \((5-\sqrt2)(1+3\sqrt2)=c+k\sqrt2\). Find c and k. [2]

(a) Simplify \(\sqrt{27}+\sqrt{12}\). [2]

(b) \(\frac{40\sqrt8}{5\sqrt2}=k\), where k is an integer. Find k. [2]

(c) Rationalise \(1/(3-\sqrt5)\). [2]

\(\frac{16^{5m}}4=64^{2n}\). Find m in terms of n. [3]

(a) Simplify \(3t^5\times5t^3\). [2]

(b) Simplify \((64u^{36})^{5/6}\). [2]

Find k if \(\sqrt{\frac{10^{400}}{10^{220}\times10^{80}}}=10^k\). [3]

A titanium atom has mass \(7.95\times10^{-23}\) grams. Find the number of atoms in 1 kg of titanium, in standard form. [2]

(a) Simplify \(5x^5y\times7x^3y^2\). [2]

(b) Find n if \(7^n=\sqrt[5]{7}\). [1]

Solve \((1/3)^x=9^{x+4}\). [3]

Rationalise and simplify \(20/(4+\sqrt6)\). [3]

\(27^{nx}=(9^x)^2\). Find n. [2]

\(n^{15}\div n^x=n^5\). Find x. [1]

(a) Write 66000 in standard form. [1]

(b) Calculate \((3.7\times10^8)+(3.7\times10^7)\), giving standard form. [2]

(a) \((3-\sqrt5)(2+3\sqrt5)=a+b\sqrt5\). Find a and b. [2]

(b) Rationalise \(6/\sqrt2\), giving simplest form. [2]

(a) Find \(5^{-5}\times5^5\). [1]

(b) Find \(125^{2/3}\). [2]

(a) Find \(3^2\div3^{-2}\). [2]

(b) Find \(16^{-3/2}\). [2]

(a) Find \(73^0\). [1]

(b) Find \(7/3^{-2}\). [2]

(c) Write \(27\times81^2\) as \(3^n\). [2]

(a) Simplify \(\sqrt{125}-\sqrt{20}\). [2]

(b) The rectangle area is k cm². Find k. [2]

(c) Rationalise \(1/(\sqrt7+2)\). [2]

The point (5,1024) lies on \(y=c^x\), where c is a whole number. Find y when x=−2. [3]

Choose from \(2.89\times10^{-1},\ 1.3\times10^{12},\ 8.3\times10^1,\ 9\times10^{11},\ 2.03\times10^{-5},\ 0.3\times10^{-2}\).

State which is not in standard form, which is largest, and which is smallest. [2]

Simplify.

(a) \(y^5/y^2\) [1]

(b) \(3x^3\times5x^5\) [2]

(a) \(\sqrt[5]3=3^h\). State h. [1]

(b) Simplify \((4x^3)^3\). [2]

Write 174000 in standard form. [1]

Simplify.

(a) \(\frac{32g^{16}}{16g^8}\) [2]

(b) \((625k^8)^{3/4}\) [2]

Calculate and give each answer in standard form.

(a) \((2.1\times10^{101})(8\times10^{101})\) [2]

(b) \((2.1\times10^{101})+(2.1\times10^{100})\) [2]

Simplify.

(a) \(18x^{18}\div3x^3\) [2]

(b) \((125y^{75})^{2/3}\) [2]

Simplify \((3125w^{3125})^{1/5}\). [2]

Work out \(0.3^2\) and write your answer in standard form. [2]

Simplify \((81x^{12})^{3/4}\). [2]

Simplify \(d^8\div d^2\). [1]

(a) Simplify \(n^5\times n\). [1]

(b) Simplify \(8x^6\div2x^2\). [2]

(c) Simplify \((243y^{20})^{2/5}\). [2]

(a) Find \(p\) if \(3^{3p}\times3^{2p}=729\). [2]

(b) Simplify \((32x^{10})^{1/5}\). [2]

(a) Simplify \((64y^{27})^{2/3}\). [2]

(b) Simplify \(\frac{x-5}{x^2-25}\). [2]

Planet data:

(a(i)) Write Mars’s average distance from the Sun as an ordinary number. [1]

(a(ii)) Uranus has diameter 35.8% of Jupiter’s. Find its diameter. [2]

(a(iii)) Write Neptune’s diameter : Saturn’s diameter as \(1:n\); find \(n\). [1]

(a(iv)) Find Neptune’s average Sun distance as a percentage of Earth’s. [2]

(a(v)) Jupiter’s average Sun distance is 5.20 astronomical units (AU). Find Mars’s average Sun distance in AU. [2]

(a(vi)) Mars’s diameter is 39.2% greater than Mercury’s. Find Mercury’s diameter. [2]

(b(i)) A light year is the distance light travels in 365.25 days, at \(2.9979\times10^5\text{ km/s}\). Show one light year is \(9.461\times10^{12}\text{ km}\) to 4 significant figures. [2]

(b(ii)) Andromeda is \(2.40\times10^{19}\text{ km}\) from Earth. Find the light travel time in millions of years. [2]

(a) Simplify \(h^2\times h^5\). [1]

(b) Simplify \((7/x)^{-3}\). [1]

(c) \(a^8\div a^p=a^2\). Find \(p\). [1]

Calculate \(2\times10^{100}-2\times10^{98}\) in standard form. [2]

\(4^x=1/64\). Find \(x\). [1]

Calculate \(4^5-5^4\). [1]

Simplify fully \((216y^{216})^{2/3}\). [2]

Find \(p\) when \(6^p\times6^4=6^{28}\). [1]

Find \(\sqrt{68}\times\sqrt{153}\). [1]

Find \(m\) when \(m^{-1/4}=27m^{-1}\). [3]

(a) Simplify \(y^3\div y^5\). [1]

(b) Simplify \(7x^0\). [1]

Simplify \(18x^{18}\div9x^9\). [2]

Simplify \((3125x^{3125})^{1/5}\). [2]

(a) Simplify fully \((81x^{16})^{3/4}\). [2]

(b) Simplify fully \(\left(\frac1{y^2}\right)^{-1/2}\). [1]

(a(i)) Round 2994.99 to the nearest 10. [1]

(a(ii)) Round 0.983 to 1 decimal place. [1]

(a(iii)) Round 2090 to 2 significant figures. [1]

(b) Write a prime between 90 and 100. [1]

(c) Write \(2^{-6}\) as a fraction. [1]

(d) Write 0.00701 in standard form. [1]

(e) Simplify \(1.5\times10^x+1.5\times10^{x-1}\) in standard form. [2]

(f) Convert \(0.3\dot7\) to a fraction, showing working. [2]

Simplify \((343x^9)^{2/3}\). [2]

Calculate \(4.8\times10^6+3.7\times10^7\). Give standard form. [1]

Calculate \(\sqrt[4]{.0256}\). [1]

Simplify \(3x^3\times4x^4\). [2]

Simplify \(2.1\times10^p+2.1\times10^{p-1}\) and give standard form. [2]

(a) Simplify \((4ab^5)^4\). [2]

(b) Solve \(2p^{1/3}=6\). [1]

(c) Solve \(81^2\div3^t=9\). [2]

(a) Write 0.00654 in standard form. [1]

(b) Write \(1.467\times10^{102}\) as an ordinary number. How many zeros follow the digit 7? [1]

(a(i)) Simplify \(7^5\times7^6\) as a single power of 7. [1]

(a(ii)) Simplify \(7^{15}\div7^5\) as a single power of 7. [1]

(a(iii)) Write 42 + 7 as a single power of 7. [1]

(b) Simplify \((5x^2\times2xy^4)^3\). [3]

(c(i)) Given \(P=2^5\times3^3\times7\) and Q = 540, find their HCF. [2]

(c(ii)) Find their LCM. [2]

(c(iii)) Find the smallest positive integer R for which PR is a cube number. [2]

(d(i)) Factorise \(x^2-3x-28\) completely. [2]

(d(ii)) Factorise \(7(a+2b)^2+4a(a+2b)\) completely. [2]

(e) Given \(3^{2x-1}=\frac1{9^x}\times3^{2y-x}\), express y in terms of x. [4]

Calculate \(\sqrt[4]{39\frac1{16}}\). [1]

Calculate \(0.04^2+0.03\times0.28\) and give the answer in standard form. [2]

Simplify fully \((243y^{10})^{3/5}\). [2]

Simplify \(32g^{32}\div4g^4\). [2]

(a) Simplify \(\frac{x^{2/3}}{x^{8/3}}\). [1]

(b) Given \(16=64^k\), find k. [1]

(c) Solve \(3^{3x}\left(\frac19\right)^{4-3x}=3\). [3]

(a) Write \(243\times27^{2n}\) as a single power of 3 in terms of n. [2]

(b) Given \(k=2\times3^2\times p^3\), where p is prime and greater than 3, write \(6k^2\) as a product of prime factors. [2]

Calculate \((2.3\times10^{-3})+(6.8\times10^{-4})\). Give your answer in standard form. [1]

Simplify \(8t^8\div4t^4\). [2]

Calculate \((3\times10^{-3})^3\) in standard form. [1]

(a) Simplify \((5x^4)^3\). [2]

(b) Simplify \((256x^{256})^{3/8}\). [2]

Given \(\sqrt[3]{y^2}=\sqrt[6]{x}\) and \(y=\sqrt[n]{x}\), find n. [2]

Write \(2^{-4}\) as a decimal. [1]

(a) Simplify \(p^2\times p^4\). [1]

(b) Simplify \(m^{15}\div m^5\). [1]

(c) Simplify \((k^3)^5\). [1]

Simplify \(2x^2\times5x^5\). [2]

Write \((3\times10^{199})+(2\times10^{201})\) in standard form. [2]

(a) Simplify \((4xy^2)^3\). [2]

(b) Find k in \(25=125^k\). [1]

Simplify \(a^2\div a^6\). [1]

(a) Find n when \(5^n=1/125\). [1]

(b) Simplify \(\left(\frac{64}{m^3}\right)^{-1/3}\). [2]

(a) Simplify \((81y^{16})^{3/4}\). [2]

(b) \(2^3=4^p\). Find p. [1]

(a) Simplify \(t^{21}\div t^7\). [1]

(b) Simplify \((u^5)^5\). [1]

(a) Simplify \(5m^2\times2m^3\). [2]

(b) Simplify \((x^8)^3\). [1]

(a) Solve \(5x-17=7x+3\). [2]

(b) Find integer n satisfying \(-7<4n\le8\). [3]

(c(i)) Simplify \(a^3\times a^6\). [1]

(c(ii)) Simplify \((5xy^2)^3\). [2]

(c(iii)) Simplify \(\left(\frac{27x^{12}}{64y^3}\right)^{-1/3}\). [3]

Simplify \(\left(\frac{x^3}8\right)^{-4/3}\). [2]

(a) Write 15060 in words. [1]

(b) Write 15060 in standard form. [1]

Simplify \(2x^3\times3x^2\). [2]

Write in standard form:

(a) 72 000. [1]

(b) 0.0018. [1]

(a) Find x if \(3^{-2}\times3^x=81\). [2]

(b) Find x if \(x^{-1/3}=32x^{-2}\). [3]

Write 0.0000523 in standard form. [1]

Find p when \(2^p=\frac1{8^4}\). [2]

Find the exact value of \(8^{2/3}\times49^{-1/2}\). [2]

Write 0.0000387 in standard form. [1]

Find q when \(3^{-q}\times\frac1{27}=81\). [2]

\(3.4\times10^{-1},\quad1.36\times10^6,\quad7.9\times10^0,\quad2.4\times10^5,\quad5.21\times10^{-3},\quad4.3\times10^{-2}\).

(a) Write the largest number. [1]

(b) Write the smallest number. [1]

(a) Write \(4.82\times10^{-3}\) as an ordinary number. [1]

(b) Write 52 million in standard form. [1]

(a) Find \(\left(\frac1{81}\right)^{-3/4}\). [1]

(b) Simplify \(\sqrt[3]{27t^{27}}\). [2]

(a(i)) Simplify \((3p^2)^5\). [2]

(a(ii)) Simplify \(18x^2y^6\div2xy^2\). [2]

(a(iii)) Simplify \(\left(\frac5m\right)^{-2}\). [1]

All lengths are metres; rectangle area=310 m².

(b) Find w. [4]

Calculate \((6.4\times10^7)+(9.6\times10^6)\); give standard form. [2]

Write 23 000 in standard form. [1]

Calculate \(0.125^{-2/3}\). [1]

(a) Find x when \(t^x t^2=t^{10}\). [1]

(b(i)) Simplify \(\left(\frac4x\right)^{-2}\). [1]

(b(ii)) Simplify \(a^3b^7\div a^6b^2\). [2]

(a) Simplify \(\frac{w^2}{w^3}\). [1]

(b) Simplify \((3w^3)^3\). [2]

Work out \(\left(\frac{125}{27}\right)^{-2/3}\). [1]

(a) Write five million, two hundred and seven in figures. [1]

(b) Write 0.00813 in standard form. [1]

Work out.

(a) \(t^{24}\div t^4\). [1]

(b) \((x^5)^2\). [1]

(c) \((81m^8)^{3/4}\). [2]

Simplify \((x^2)^5\). [1]

One sheet of paper is \(8\times10^{-3}\) cm thick. Work out the thickness of 250 sheets. [1]

(a) Find r when \(2^r=\frac1{16}\). [1]

(b) Find t when \(3^t=\sqrt[5]{3}\). [1]

(a) Write 0.0605 in standard form. [1]

(b) Calculate \(0.1\times5.1\times10^4\) in standard form. [1]

Work out.

(a) \(125^{2/3}\). [1]

(b) \((\frac13)^{-2}\). [1]

(a) Simplify \((16x^{16})^{3/4}\). [2]

(b) Find p when \(2p^{3/2}=54\). [2]

Simplify \((\frac8{a^{12}})^{1/3}\). [2]

Simplify.

(a) \(6w^0\). [1]

(b) \(5x^3-3x^3\). [1]

(c) \(3y^6\times5y^{-2}\). [2]

(a) Simplify \((m^5)^2\). [1]

(b) Simplify \(4x^3y\times5x^2y\). [2]

Work out \(2^{-4}\times2^5\). [1]

Write \(5.17\times10^{-3}\) as an ordinary number. [1]

(a) Simplify \(81^{3/4}\). [1]

(b) Simplify \(x^{2/3}\div x^{-4/3}\). [1]

(c) Simplify \((8/y^6)^{-1/3}\). [2]

Work out \(1.2\times10^{40}+1.2\times10^{41}\) in standard form. [2]

Calculate \(\sqrt{9+25^{-1/3}}\). [1]

Find p if \((10^3)^p=10^2\). [1]

Simplify.

(a) \(x^3y^4\times x^5y^3\). [2]

(b) \((3p^2m^5)^3\). [2]

Simplify \((16p^{16})^{\frac14}\). [2]

Write \(1.27\times10^{-3}\) as an ordinary number. [1]

Write 0.0000574 in standard form. [1]

Simplify \((\frac12x^{2/3})^3\). [2]

Simplify \((32x^{10})^{3/5}\). [2]

Find \(x\) in each equation.

(a(i)) \(3^x=243\). [1]

(a(ii)) \(16^x=4\). [1]

(a(iii)) \(8^x=32\). [2]

(a(iv)) \(27^x=\frac19\). [2]

(b) Solve \(y^2-7y-30=0\) by factorisation, showing working. [3]

Simplify \((36x^{16})^{1/2}\). [2]

Simplify \(36y^5\div4y^2\). [2]

Simplify \(n^2\times n^5\). [1]

Write in standard form:

(a) 2470000; [1]

(b) 0.0079. [1]

Order \(0.6^3,\ 0.22,\ \sqrt{0.09},\ 0.4^2\), smallest first. [2]

(a) Write \(5^{-3}\) as a fraction. [1]

(b) Write 0.00456 in standard form. [1]

Simplify:

(a(i)) \(x^0\); [1]

(a(ii)) \(m^4\times m^3\); [1]

(a(iii)) \((8p^6)^{1/3}\). [2]

(b) Given \(243^x=3^2\), find x. [2]

Write 270000 in standard form. [1]

Simplify \(6uw^{-3}\times4uw^6\). [2]

Write 53400000 in standard form. [1]

(a(i)) Find \((1/4)^{0.5}\). [1]

(a(ii)) Find \((-8)^{2/3}\). [1]

(b) Use a calculator to find \(\frac{\sqrt{29-3\times32^{0.4}}}{3}\). [1]

Solve \(81^x=3\). [1]

Simplify:

(a) \(12x^{12}\div3x^3\); [2]

(b) \((256y^{256})^{1/8}\). [2]

Simplify \(\left(\frac{x^{64}}{16y^{16}}\right)^{1/4}\). [3]

Write \(1.7\times10^{-4}\) as an ordinary number. [1]

(a) Evaluate \((\sqrt5)^8\). [1]

(b) Evaluate \((1/27)^{-2/3}\). [1]

\(p=4\times10^5,\ q=5\times10^4\). Give in standard form:

(a) pq; [2]

(b) q/p. [2]

(a) \((2^{24})^{1/2}=p^4\). Find p. [2]

(b) Simplify \(\frac{q^2+q^2}{q^{1/4}\times q^{1/4}}\). [3]

Order from smallest: \(0.5^2,\ 0.5,\ 0.5^3,\ \sqrt[3]{0.5}\). [2]

(a) Round 569000 to 2 significant figures. [1]

(b) Write 569000 in standard form. [1]

(a) Simplify \((3125t^{125})^{1/5}\). [2]

(b) Find p when \(3^p=1/9\). [1]

(c) Find w when \(x^{72}/x^w=x^8\). [1]

(a) Calculate \(7.5^{-0.4}/\sqrt{57}\) and write your full calculator display. [1]

(b) Write the answer in standard form. [1]

(a) Simplify \(x^8\div x^2\). [1]

(b) Simplify \((x^6/27)^{1/3}\). [2]

(a) Write \(2.8\times10^2\) as an ordinary number. [1]

(b) Calculate \((2.5\times10^8)(2\times10^{-2})\) in standard form. [2]

Calculate \((4\times10^{-5})(6\times10^{12})\) in standard form. [2]

(a(i)) Simplify \(x^3\div\frac3{x^5}\). [1]

(a(ii)) Simplify \(5xy^8\times3x^6y^{-5}\). [2]

(a(iii)) Simplify \((64x^{12})^{2/3}\). [2]

(b) Solve \(3x^2-7x-12=0\) with working, to 2 decimal places. [4]

(c) Simplify \((x^2-25)/(x^3-5x^2)\). [3]

Simplify \((27x^{12})^{1/3}\). [2]

Calculate \((4.3\times10^8)+(2.5\times10^7)\) in standard form. [2]

Order these from smallest to largest: \((1.5)^{2/3},\ (2/3)^{1.5},\ (2/3)^{-1.5},\ (-2/3)^{2/3}\). [2]

(a) Calculate \(2(5.5\times10^4)\) in standard form. [2]

(b) Calculate \((5.5\times10^4)-(5\times10^4)\) in standard form. [2]

(a) \(3^x=\sqrt[4]{3^5}\). Find x. [1]

(b) Simplify \((32y^{15})^{2/5}\). [2]

Order from smallest to largest: \(19\%,\ 1/5,\ \sqrt{0.038},\ \sin11.4^\circ,\ 0.719^5\). [2]

(a) Calculate 600 ÷ 8000 in standard form. [2]

(b) Calculate \(10^8-7\times10^6\) in standard form. [2]

(a) Simplify \((64q^{-2})^{1/2}\). [2]

(b) \(5^7\div5^9=p^2\). Find p. [2]

Find r if \(5^{r/3}=125\). [2]

(a) Simplify \((4pq^2)^3\). [2]

(b) Simplify \((16x^8)^{-1/4}\). [2]

A football match ticket costs \$124.

(a) Calculate the receipts when 76 500 tickets are sold. [1]

(b) Write the amount in standard form. [1]

Simplify \((a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})\). [2]

(a) \((3/8)^{3/8}(3/8)^{1/8}=p^q\). Find p and q. [2]

(b) \(5^{-3}+5^{-4}=k\times5^{-4}\). Find k. [2]

Without a calculator, show all working to establish \((49/16)^{-3/2}=64/343\). [2]

Simplify \((256w^{256})^{1/4}\). [2]

Calculate \(81^{0.25}\div4^{-2}\). [2]

(a) Find m when \(4^m4^2=4^{12}\). [1]

(b) Find p when \(6^p\div6^5=\sqrt6\). [1]

Solve \(4x+6\times10^3=8\times10^4\) and give x in standard form. [3]

(a) Simplify \((3x^3)^3\). [2]

(b) Simplify \((125x^6)^{2/3}\). [2]

A hummingbird beats its wings 24 times per second.

(a) Find the number of wing beats in one hour. [1]

(b) Write this in standard form. [1]

(a) Simplify \(32x^8\div8x^{32}\). [2]

(b) Simplify \((x^3/64)^{2/3}\). [2]

(a) Write 16 460 000 in standard form. [1]

(b) Calculate \(7.85/(2.366\times10^2)\) in standard form. [2]

Work out \(2(3\times10^8-4\times10^6)\), giving the answer in standard form. [2]

(a) Calculate \(3^0\times2.5^2\). [1]

(b) Calculate \(2.5^{-2}\). [1]

Evaluate \((27/8)^{-4/3}\) as an exact fraction. [2]

Show every step to prove \(3^{-2}+2^{-2}=13/36\). [2]

(a) Find m if \(2^m=0.125\). [2]

(b) Find n if \(2^{4n}\times2^{2n}=512\). [2]

Calculate \(5(6\times10^3+400)\) and give the answer in standard form. [2]

Order these from smallest to largest: \(2/\sqrt3,\ 2-\sqrt3,\ \sqrt3,\ 2-\sqrt3/2\). [2]

Write \(2^8\times8^2\times4^{-2}\) in the form \(2^n\). [2]

Given \(3^x\times9^4=3^n\), express n in terms of x. [2]