Question

Need help, I cant simplify this

Answer 1

`7^{(2)/(5)}`

Explanation:

Step 1: First apply radical rule in the given expression.

`\sqrt[n]{a}=a^{(1)/(n)}`

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

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

Step 2: Now, apply exponent rule in the above expression

`(x^(m))/(x^(n))=x^(m-n)`

So, the expression becomes,
`7^{\left((1)/(3)-(1)/(5)\right)}`.

Step 3: Take cross multiply the denominator and numerator of the fraction in the power of 7.

`\Rightarrow 7^{\left((1)/(3)-(1)/(5)\right)}=7^{\left((5-3)/(15)\right)}=7^{(2)/(5)}`

The answer is
`7^{(2)/(5)}`.

Hence the simplified form of
`\frac{\sqrt[3]{7}}{\sqrt[5]{7}}=7^{(2)/(5)}`.