Question

Write the expression as a radical.

Answer 1

Answer:

$5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}$

Step-by-step explanation:

Let us consider the expression

$5\sqrt{5}\left(ab\right)^{\frac{3}{2}}$

Writing the expression as a radical

But, let us revise some rules:

$\sqrt{a}=a^{\frac{1}{2}}$

$\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0$

$\left(a\cdot \:b\right)^n=a^nb^n$

let us solve now

$5\sqrt{5}\left(ab\right)^{\frac{3}{2}}$

$=5^{\frac{3}{2}}\left(ab\right)^{\frac{3}{2}}$         ∵  $\:5^{\frac{3}{2}}=5\sqrt{5}$

$=\left(5ab\right)^{\frac{3}{2}}$

$=\left(5ab\right)^{3\cdot \frac{1}{2}}$

$=\left(\left(5ab\right)^3\right)^{\frac{1}{2}}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}=a^{\frac{1}{2}}$

$=\sqrt{\left(5ab\right)^3}$

Thus,

$5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}$