Question

Compute:
$(243{)}^{\frac{2}{5}}\times (32{)}^{\frac{2}{5}}$

• A. $40$
• B. $48$
• C. $16$
• D. $36$

Answer 1

The correct option is D $36$

As given ${\left(243\right)}^{\frac{2}{5}}+{\left(32\right)}^{-\frac{2}{5}}$
We can write 243 as $3^{5}and32as{2}^5$
$\Rightarrow {\left(3^5\right)}^{\frac{2}{5}}+{\left(2^5\right)}^{-\frac{2}{5}}$
$\Rightarrow \left(3^{5\cdot \frac{2}{5}}\right)+\left(2^{5\cdot -\frac{2}{5}}\right)$
$\Rightarrow 3^2+2^{-2}$
$\Rightarrow 9+\frac{1}{2^2}$
$\Rightarrow 9+\frac{1}{4}$
$\Rightarrow \frac{36+1}{4}$
$\Rightarrow \frac{37}{4}$