Question

Write the value of ${\left\{5{(8^{\frac{1}{3}}+{27}^{\frac{1}{3}})}^3\right\}}^{\frac{1}{4}}$

Answer 1

${\left\{5{(8^{\frac{1}{3}}+{27}^{\frac{1}{3}})}^3\right\}}^{\frac{1}{4}}=5^{\frac{1}{4}}{(8^{\frac{1}{3}}+{27}^{\frac{1}{3}})}^{3\times \frac{1}{4}}=5^{\frac{1}{4}}{(8^{\frac{1}{3}}+{27}^{\frac{1}{3}})}^{\frac{3}{4}}=5^{\frac{1}{4}}{\left(\right(2^3{)}^{\frac{1}{3}}+\left(3^3{)}^{\frac{1}{3}}\right)}^{\frac{3}{4}}=5^{\frac{1}{4}}(2+3{)}^{\frac{3}{4}}=5^{\frac{1}{4}}\times 5^{\frac{3}{4}}=5^{\frac{1}{4}+\frac{3}{4}}=5^1=5$