Question

Simplify the following:

$\sqrt[6]{6256}÷\sqrt[3]{32}$.

• A. $2$
• B. $3$
• C. $1$
• D. $4$

Answer 1

The correct option is A $2$

$\sqrt[6]{6256}÷\sqrt[3]{32}$
$=\frac{{(2\times 2\times 2\times 2\times 2\times 2\times 2\times 2)}^{\frac{1}{6}}}{{\left(2\right)}^{\frac{1}{3}}}$
$=\frac{{\left(2^8\right)}^{\frac{1}{6}}}{{\left(2\right)}^{\frac{2}{6}}}$ $={\left(\frac{2^8}{2^2}\right)}^{\frac{1}{6}}$
$={\left(2^6\right)}^{\frac{1}{6}}$ $=2$.

Therefore, option $A$ is correct.