Question

Write the expression as a radical.

Answer 1

`5√(5)\left(ab\right)^{(3)/(2)}=√(\left(5ab\right)^3)`

Explanation:

Let us consider the expression

`5√(5)\left(ab\right)^{(3)/(2)}`

Writing the expression as a radical

But, let us revise some rules:

`√(a)=a^{(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√(5)\left(ab\right)^{(3)/(2)}`

`=5^{(3)/(2)}\left(ab\right)^{(3)/(2)}` ∵
`\:5^{(3)/(2)}=5√(5)`

`=\left(5ab\right)^{(3)/(2)}`

`=\left(5ab\right)^{3\cdot (1)/(2)}`

`=\left(\left(5ab\right)^3\right)^{(1)/(2)}`

`\mathrm{Apply\:radical\:rule}:\quad √(a)=a^{(1)/(2)}`

`=√(\left(5ab\right)^3)`

Thus,

`5√(5)\left(ab\right)^{(3)/(2)}=√(\left(5ab\right)^3)`