Question

the value of (-2/3) power 4 is equal to​

Answer 1

(-2/3)^4

= (-2^4 / 3^4)

= (16/81)

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Answer 2

$\displaystyle \sf{ {\bigg( - \frac{2}{3} \bigg)}^{4} } = \bf \frac{16}{81}$

Given :

$\displaystyle \sf{ {\bigg( - \frac{2}{3} \bigg)}^{4} }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ {\bigg( - \frac{2}{3} \bigg)}^{4} }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ {\bigg( - \frac{2}{3} \bigg)}^{4} }$

$\displaystyle \sf{ = {( - 1)}^{4} \times {\bigg( \frac{2}{3} \bigg)}^{4} \: \: \: \bigg[ \because\: {(ab)}^{n} = {a}^{n} \times {b}^{n} \: \bigg] }$

$\displaystyle \sf{ = {\bigg( \frac{2}{3} \bigg)}^{4} }$

$\displaystyle \sf{ = \frac{ {2}^{4} }{ {3}^{4} } \: \: \: \bigg[ \: \because \:{\bigg( \frac{a}{b} \bigg)}^{n} = \frac{ {a}^{n} }{ {b}^{n} } \bigg] }$

$\displaystyle \sf{ = \frac{2 \times 2 \times 2 \times 2}{3 \times 3 \times 3 \times 3} }$

$\displaystyle \sf{ = \frac{16}{81} }$

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