Question

Simplified value of ${\left(25\right)}^{\frac{1}{3}}\times 5^{\frac{1}{3}}$ is
(a) 25
(b) 3
(c) 1
(d) 5

Answer 1

$$\begin{gathered} {\left(25\right)}^{\frac{1}{3}}\times 5^{\frac{1}{3}}={\left(5^2\right)}^{\frac{1}{3}}\times 5^{\frac{1}{3}} \\ =5^{\frac{2}{3}}\times 5^{\frac{1}{3}} \\ =5^{\frac{2}{3}+\frac{1}{3}} \\ =5^{\frac{2+1}{3}} \\ =5^{\frac{3}{3}} \\ =5 \end{gathered}$$

$\therefore$Simplified value of ${\left(25\right)}^{\frac{1}{3}}\times 5^{\frac{1}{3}}$ is 5.

Hence, the correct option is (d).