# Laws of Exponents - Taking Power of a Power

## Formula

If a is a non-zero rational number and m and n are integers, then (am)n = am × n = amn.

## Notes

### Taking Power of a Power:

If a is a non-zero rational number and m and n are integers, then (am)n = am × n = amn.

(i) (32)4

= 32 × 32 × 32 × 32

= 32 + 2 + 2 + 2

= 38.....(Observe 8 is the product of 2 and 4).

= 32 × 4..............[ (am)n = am × n ]

(ii) (72)10

= 72 × 10

= 720..............[ (am)n = am × n ]

(iii) (34)3

= 34 × 3

= 312 ................[ (am)n = am × n ]

## Example

Solve: ((2/5)^(-2))^3.

((2/5)^(-2))^3.

= (2/5)^(- 2) xx (2/5)^(- 2) xx (2/5)^(- 2)

= (2/5)^((- 2) + (- 2) + (- 2))

= (2/5)^(-6).

## Example

Solve: (7^(- 2))^(-5)

(7^(- 2))^(-5)

= 1/(7^(- 2))^5

= 1/(7^(- 2)  xx  7^(- 2)  xx  7^(- 2)  xx  7^(- 2)  xx  7^(- 2))

= 1/(7^((- 2) xx 5))

= 1/7^(- 10)

= 7^10.

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