Question

Which is equivalent to 243 2/5? 3 6 9 12

Answer 1

$243^{ \frac{2}{5} } = ( \sqrt[5]{243} )^{2} = 3^{2} =9$

Answer 2

ANSWER

${(243)}^{ \frac{2}{5} } = 9$


EXPLANATION

We want to simplify the exponential expression,


${(243)}^{ \frac{2}{5} }$


We use the laws of indices to simplify the expression.



We rewrite the above expression to obtain,

${(243)}^{ \frac{2}{5} } = {(243)}^{ \frac{1}{5} \times 2 }$

Recall that,


${a}^{mn} = ( {a}^{m} ) ^{n}$


When we apply the above property, we get

${(243)}^{ \frac{2}{5} } = {( {(243)}^{ \frac{1}{5} } )}^{2}$


Now we need to write
$243$
as a certain number to the exponent of 5.



In order words,

$243 = 3 \times 3 \times 3 \times 3 \times 3 = {3}^{5}$



This implies that,


${(243)}^{ \frac{2}{5} } = {( { {3}^{5} }^{ \times \frac{1}{5} } )}^{2}$



We further simplify to get,


${(243)}^{ \frac{2}{5} } = 3^{2}$


This will finally evaluate to,


${(243)}^{ \frac{2}{5} } = 9$