Question

How do you simplify `64^(-4/3)`?

Answer 1

`1/256`

Explanation:

Using the `color(blue)"law of exponents"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(a^(m/n)=(root(n)(a))^m" and "a^-mhArr1/a^m)color(white)(2/2)|)))`

`rArr64^(-4/3)`

`=1/(64^(4/3))`

`=1/(root(3)(64))^4`

`=1/(4)^4`

`=1/256`