Question

how to solve

Answer 1

Recall that \(\large\left(a^b\right)^c=a^{bc}\), that \(\large a^ba^c=a^{b+c}\), and that \(\large \sqrt[b]{a}=a^{1/b}\).

So,
\[\large\sqrt[3]{a^{14}b^7}=\left(a^{14}b^7\right)^{1/3}=a^{14/3}b^{7/3}\]
Dividing, you have \(\dfrac{14}{3}=4+\dfrac{2}{3}\) and \(\dfrac{7}{3}=2+\dfrac{1}{3}\).
\[\large a^{14/3}b^{7/3}=a^{4+2/3}b^{2+1/3}=a^4a^{2/3}b^2b^{1/3}=a^4b^2\sqrt[3]{a^2b}\]

Answer 2

thanks but can you do it without fraction?