Laws of indices worksheets with answers

Cambridge IGCSE 0580

Combine, simplify and evaluate powers, from the basic laws to negative and fractional indices.

Sample sheet

Laws of indices, Standard

Name Date

1
Work out $2^{-3}$ . Give your answer as a fraction.
[2]
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2
Work out $25^{\frac{3}{2}}$ .
[2]
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3
Work out $\frac{2^{7} \times 2^{4}}{2^{10}}$ . Give your answer as an integer or a fraction.
[3]
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4
Work out $2^{-1}$ . Give your answer as a fraction.
[2]
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5
Work out $4^{-1}$ . Give your answer as a fraction.
[2]
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6
Work out $3^{-2}$ . Give your answer as a fraction.
[2]
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Answers

Laws of indices, Standard

1 $\frac{1}{8}$
2 $125$
3 $2$
4 $\frac{1}{2}$
5 $\frac{1}{4}$
6 $\frac{1}{9}$

Method in brief

Add the indices when multiplying powers of the same base, subtract when dividing, multiply when raising a power to a power. A negative index means a reciprocal and a fractional index means a root.

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More worksheets

Laws of indices worksheets with answers

Cambridge IGCSE 0580

Combine, simplify and evaluate powers, from the basic laws to negative and fractional indices.

Sample sheet

Laws of indices, Standard

Name Date

1
Work out $2^{-3}$ . Give your answer as a fraction.
[2]
Scan for help
2
Work out $25^{\frac{3}{2}}$ .
[2]
Scan for help
3
Work out $\frac{2^{7} \times 2^{4}}{2^{10}}$ . Give your answer as an integer or a fraction.
[3]
Scan for help
4
Work out $2^{-1}$ . Give your answer as a fraction.
[2]
Scan for help
5
Work out $4^{-1}$ . Give your answer as a fraction.
[2]
Scan for help
6
Work out $3^{-2}$ . Give your answer as a fraction.
[2]
Scan for help

Answers

Laws of indices, Standard

1 $\frac{1}{8}$
2 $125$
3 $2$
4 $\frac{1}{2}$
5 $\frac{1}{4}$
6 $\frac{1}{9}$

Method in brief

Add the indices when multiplying powers of the same base, subtract when dividing, multiply when raising a power to a power. A negative index means a reciprocal and a fractional index means a root.

Learn the method

Stuck on a question?

Scan the code beside a question to get help with it.

Open the tutor