Question

Explain why 27^2/3 equals 9

Answer 1

As we know that , According to the rules of exponent

a⅔ can be written as ( a⅓)² So ,

(27⅓)²

Now according to the rule of roots we can write

`{(a)}^{ (1)/(3) } = \sqrt[3]{a} \\`

Then similarly :-

`{( \sqrt[3]{27} )}^(2) = ( {3)}^(2) \\`

(3)² = 3×3

= 9

Hence proved .