Question

Evaluate:
${\left[5{(8^{\frac{1}{3}}+{27}^{\frac{1}{3}})}^3\right]}^{\frac{1}{4}}$

Answer 1

${\left[5{(8^{\frac{1}{3}}+{27}^{\frac{1}{3}})}^3\right]}^{\frac{1}{4}}=x$

We know that

$2^3=8$

$8^{\frac{1}{3}}=2$

$3^3=27$

${27}^{\frac{1}{3}}=3$

$x=\left[5\right(2+3{)}^3{]}^{\frac{1}{4}}=\left[5\right(5{)}^3{]}^{\frac{1}{4}}$

$x=[5^4{]}^{\frac{1}{4}}$

$x=5$.