Question

Simplified value of $(25{)}^{\frac{1}{3}}\times (5{)}^{\frac{1}{3}}$ is :

• A. $25$
• B. $3$
• C. $1$
• D. $5$

Answer 1

The correct option is D $5$

$\Rightarrow$ $(25{)}^{\frac{1}{3}}\times (5{)}^{\frac{1}{3}}$

$\Rightarrow$ $\left(\right(5{)}^2{)}^{\frac{1}{3}}\times (5{)}^{\frac{1}{3}}$

$\Rightarrow$ $(5{)}^{\frac{2}{3}}\times (5{)}^{\frac{1}{3}}$

$\Rightarrow$ $(5{)}^{\frac{2}{3}+\frac{1}{3}}$ $[\because x^m\times x^n=x^{m+n}]$

$\Rightarrow$ $(5{)}^{\frac{3}{3}}$

$\Rightarrow$ $(5{)}^1=5$

$\therefore$ $(25{)}^{\frac{1}{3}}\times (5{)}^{\frac{1}{3}}=5$