Question

`[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9` = ______.

Answer 1

`[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9` = `underlinebb((2/13)^-36)`.

Explanation:

Using laws of exponents,

a^m ÷ aⁿ = (a)^{m – n} and a^m × aⁿ = (a)^{m + n}  ...[∵ a is non-zero integer]

∴ `[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9 = [(2/13)^(-6  -  3)]^3 xx (2/13)^-9`

= `(2/13)^-27 xx (2/13)^-9`

= `(2/13)^(-27  -  9)`

= `(2/13)^-36`

Hence, `[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9 = (2/13)^-36`