Answer:
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}[/tex]
Step-by-step explanation:
Let us consider the expression
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}[/tex]
Writing the expression as a radical
But, let us revise some rules:
[tex]\sqrt{a}=a^{\frac{1}{2}}[/tex]
[tex]\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]
[tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]
let us solve now
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}[/tex]
[tex]=5^{\frac{3}{2}}\left(ab\right)^{\frac{3}{2}}[/tex] ∵ [tex]\:5^{\frac{3}{2}}=5\sqrt{5}[/tex]
[tex]=\left(5ab\right)^{\frac{3}{2}}[/tex]
[tex]=\left(5ab\right)^{3\cdot \frac{1}{2}}[/tex]
[tex]=\left(\left(5ab\right)^3\right)^{\frac{1}{2}}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}=a^{\frac{1}{2}}[/tex]
[tex]=\sqrt{\left(5ab\right)^3}[/tex]
Thus,
[tex]5\sqrt{5}\left(ab\right)^{\frac{3}{2}}=\sqrt{\left(5ab\right)^3}[/tex]
