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Laws of Exponents - Taking Power of a Power

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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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