Question

Help? Very confused math is not my subject.

Answer 1

Rewrite the root expressions as fractional exponents:

$\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = \dfrac{7^{1/3}}{7^{1/5}}$

Recall that $\frac{a^m}{a^n} = a^{m-n}$, so that

$\dfrac{7^{1/3}}{7^{1/5}} = 7^{1/3 - 1/5}$

Simplify the exponent:

$\dfrac13 - \dfrac15 = \dfrac5{15} - \dfrac3{15} = \dfrac{5-3}{15} = \dfrac2{15}$

Then you end up with

$\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = 7^{2/15}$