Question

evaluate [7(64^1/3 + 27^1/3)^3]^1/4​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ { \bigg[ 7 {( {64}^{ \frac{1}{3} } + {27}^{ \frac{1}{3} })}^{3} \bigg] }^{ \frac{1}{4} } }$

EVALUATION

$\displaystyle \sf{ { \bigg[ 7 {( {64}^{ \frac{1}{3} } + {27}^{ \frac{1}{3} })}^{3} \bigg] }^{ \frac{1}{4} } }$

$\displaystyle \sf{ = { \bigg[ 7 \times { \Bigg( {({4}^{3}) }^{ \frac{1}{3} } + {( {3}^{3}) }^{ \frac{1}{3} } \Bigg)}^{3} \bigg] }^{ \frac{1}{4} } }$

$\displaystyle \sf{ = { \bigg[ 7 \times {{ \Bigg( 4 +3 \Bigg)}^{3} }\bigg] }^{ \frac{1}{4} } }$

$\displaystyle \sf{ = { \bigg[ 7 \times {7}^{3} \bigg] }^{ \frac{1}{4} } }$

$\displaystyle \sf{ = { \bigg[ {7}^{4} \bigg] }^{ \frac{1}{4} } }$

$= 7$

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