Question

Help? Very confused math is not my subject.

Answer 1

Rewrite the root expressions as fractional exponents:

`\frac{\sqrt[3]{7}}{\sqrt[5]{7}} = (7^(1/3))/(7^(1/5))`

Recall that
`(a^m)/(a^n) = a^(m-n)`, so that

`(7^(1/3))/(7^(1/5)) = 7^(1/3 - 1/5)`

Simplify the exponent:

`\frac13 - \frac15 = \frac5{15} - \frac3{15} = (5-3)/(15) = \frac2{15}`

Then you end up with

`\frac{\sqrt[3]{7}}{\sqrt[5]{7}} = 7^(2/15)`