Exam-Style Problems

Stage 9 - Q1 - 2 marks

18977

Evaluate.

\[8^0\]

Hint

Compare a power divided by itself.

Stage 9 - Q2 - 2 marks

18978

Evaluate as an exact fraction.

\[10^{-4}\]

Hint

First write a reciprocal with a positive power.

Stage 9 - Q3 - 3 marks

18979

Write as a power of 10.

\[0.1\]

Hint

Count the decimal places to the nonzero digit.

Stage 9 - Q4 - 3 marks

18980

Evaluate. Keep the negative base in brackets.

\[(-3)^{-2}\]

Hint

An even power of a negative base is positive.

Stage 9 - Q5 - 4 marks

18981

Find the missing integer exponent.

\[6^n=\frac{1}{216}\]

Hint

The reciprocal changes the sign of the index.

Stage 9 - Q6 - 4 marks

18982

Find the missing integer exponent.

\[7^n=\frac{1}{2401}\]

Hint

The reciprocal changes the sign of the index.

Stage 9 - Q7 - 5 marks

18983

Evaluate exactly when \(x=9\).

\[x^2+x^{-2}\]

Hint

The negative index does not make the term negative.

Stage 9 - Q8 - 5 marks

18984

Compare the two values.

\[11^{-4},\quad -11^4\]

Hint

Distinguish an exponent sign from a sign in front of a power.

Stage 9 - Q9 - 5 marks

18985

A learner writes \(2^{-1}=-2\). Explain the error and give the correct value.

Hint

Use the pattern obtained by dividing by the base each step.

Stage 9 - Q10 - 3 marks

18986

Find all positive integer bases b and negative integer exponents \(n\) for which \(b^n=\frac{1}{81}\).

Hint

Write 81 as powers with integer bases and then use reciprocals.