Question

Simplify ( 8^1/3+27^1/3 )^3​

Answer 1

SOLUTION

TO SIMPLIFY

$\displaystyle \sf{ {({8}^{ \frac{1}{3} } + {27}^{ \frac{1}{3} })}^{3} }$

EVALUATION

$\displaystyle \sf{ {({8}^{ \frac{1}{3} } + {27}^{ \frac{1}{3} })}^{3} }$

$\displaystyle \sf{ = { \bigg[{ ({2}^{3} )}^{ \frac{1}{3} } + { ({3}^{3}) }^{ \frac{1}{3} } \bigg]}^{3} }$

$\displaystyle \sf{ = { \bigg[{ (2)}^{ (3 \times \frac{1}{3}) } + {(3) }^{ (3 \times \frac{1}{3}) } \bigg]}^{3} }$

$\displaystyle \sf{ = { \bigg[2 + 3 \bigg]}^{3} }$

$\displaystyle \sf{ = {5}^{ 3} }$

$= 125$

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Answer 2

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