Class 8 Exponents and Powers — practice questions with answers

Exponents and Powers · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Write 5^(-2) as a fraction.

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Answer: A)

\frac{1}{25}

A negative exponent means reciprocal: 5^(-2) =

\frac{1}{5 ^{2}}

\frac{1}{25}

2. Simplify 4^(-1) x 4³ into a single power of 4.

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Answer: A) 4²

Same base, add exponents: 4^(-1 + 3) = 4² = 16.

3. Simplify

\frac{3 ^{- 3} \times 3 ^{2}}{3 ^{- 4}}

. Give the answer as a power of 3.

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Answer: A) 3³

Numerator: 3^(-3 + 2) = 3^(-1). Then

\frac{3 ^{- 1}}{3 ^{- 4}}

= 3^(-1 - (-4)) = 3³.

4. The rule

a^{0} = 1

works for every value of

a

except one. Which value has to be left out?

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Answer: A) 0

The zero-exponent law is always stated for a non-zero base, because

0^{0}

is not defined. Every other number works, including negatives and fractions:

(- 1)^{0} = 1

and

1 0^{0} = 1

5. Find the value of

\frac{2 ^{- 2} \times 3 ^{- 1}}{6 ^{- 2}}

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Answer: B) 3

The numerator is

2^{- 2} \times 3^{- 1} = \frac{1}{4} \times \frac{1}{3} = \frac{1}{12}

and

6^{- 2} = \frac{1}{36}

. Dividing by

\frac{1}{36}

means multiplying by 36, so

\frac{1}{12} \times 36 = 3

. Multiplying by

6^{- 2}

instead of dividing gives the trap

\frac{1}{432}

, and stopping after the numerator gives

\frac{1}{12}

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