Stage 9 - Q1 - 2 marks
18987
Write as one power.
\[8^{4}\times8^{-2}\]
Hint
The base stays fixed.
Stage 9 - Q2 - 2 marks
18988
Write as one power.
\[10^{-6}\div10^{-2}\]
Hint
Subtracting a negative adds.
Stage 9 - Q3 - 3 marks
18989
Write as one power.
\[(3^{-2})^{3}\]
Hint
Repeated powers multiply exponents.
Stage 9 - Q4 - 3 marks
18990
Find the integer index.
\[5^{4}\times5^n=5^{-1}\]
Hint
Use the product rule, then solve for the index.
Stage 9 - Q5 - 4 marks
18991
Write as a power of 7.
\[(49)^{-6}\]
Hint
Express the base itself as a power.
Stage 9 - Q6 - 4 marks
18992
Write as a power of 9.
\[(81)^{-2}\]
Hint
Express the base itself as a power.
Stage 9 - Q7 - 5 marks
18993
Simplify to one power.
\[\frac{2^{4}\times2^{-5}}{2^{1}}\]
Hint
Work with all three indices in order.
Stage 9 - Q8 - 5 marks
18994
Is this claim correct? Justify your answer.
\[4^{-6}+4^{-6}=4^{-12}\]
Hint
Think of two identical terms being added.
Stage 9 - Q9 - 5 marks
18995
Find the missing integer exponent.
\[\frac{6^n}{6^{-2}}=6^{1}\]
Hint
Translate the quotient into an equation in indices.
Stage 9 - Q10 - 3 marks
18996
Find the integer \(n\) that makes the equation true.
\[\frac{8^n\times2^{-3}}{4^{n-1}}=\frac1{16}\]
Hint
The common base should be 2.