Question

Simplify: (4a^5/3)^3/2

Answer 1

\[\Large \left(4a^{\frac{5}{3}}\right)^{\frac{3}{2}}\]


\[\Large 4^{\frac{3}{2}}a^{\left(\frac{5}{3}*\frac{3}{2}\right)}\]


\[\Large 4^{\frac{3}{2}}a^{\frac{5*3}{3*2}}\]


\[\Large 4^{\frac{3}{2}}a^{\frac{15}{6}}\]


\[\Large 4^{\frac{3}{2}}a^{\frac{5}{2}}\]


\[\Large \sqrt{4^3}a^{\frac{5}{2}}\]


\[\Large \sqrt{64}a^{\frac{5}{2}}\]


\[\Large 8a^{\frac{5}{2}}\]


\[\Large 8\sqrt{a^5}\]


\[\Large 8\sqrt{a^4*a}\]


\[\Large 8\sqrt{a^4}*\sqrt{a}\]


\[\Large 8a^2\sqrt{a}\]

So \[\Large \left(4a^{\frac{5}{3}}\right)^{\frac{3}{2}}=8a^2\sqrt{a}\]

Answer 2

Thank you so much!