Question

Need help, I cant simplify this

Answer 1

Answer:

$7^{\frac{2}{5}}$

Step-by-step explanation:

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

$\sqrt[n]{a}=a^{\frac{1}{n}}$

Here, $\sqrt[3]{7}=7^{\frac{1}{3}}, \sqrt[5]{7}=7^{\frac{1}{5}}$

The expression becomes $\frac{\sqrt[3]{7}}{\sqrt[5]{7}}=\frac{7^{\frac{1}{3}}}{7^{\frac{1}{5}}}$  

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

$\frac{x^{m}}{x^{n}}=x^{m-n}$  

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

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

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

The answer is $7^{\frac{2}{5}}$.

Hence the simplified form of $\frac{\sqrt[3]{7}}{\sqrt[5]{7}}=7^{\frac{2}{5}}$.