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Roman55 [17]
3 years ago
8

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

Mathematics
2 answers:
Anna11 [10]3 years ago
7 0
243^{ \frac{2}{5} } = ( \sqrt[5]{243} )^{2} = 3^{2} =9
vodomira [7]3 years ago
6 0
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

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