Answer:
[tex]7^{\frac{2}{5}}[/tex]
Step-by-step explanation:
Step 1: First apply radical rule in the given expression.
[tex]\sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
Here, [tex]\sqrt[3]{7}=7^{\frac{1}{3}}, \sqrt[5]{7}=7^{\frac{1}{5}}[/tex]
The expression becomes [tex]\frac{\sqrt[3]{7}}{\sqrt[5]{7}}=\frac{7^{\frac{1}{3}}}{7^{\frac{1}{5}}}[/tex]
Step 2: Now, apply exponent rule in the above expression
[tex]\frac{x^{m}}{x^{n}}=x^{m-n}[/tex]
So, the expression becomes, [tex]7^{\left(\frac{1}{3}-\frac{1}{5}\right)}[/tex].
Step 3: Take cross multiply the denominator and numerator of the fraction in the power of 7.
[tex]\Rightarrow 7^{\left(\frac{1}{3}-\frac{1}{5}\right)}=7^{\left(\frac{5-3}{15}\right)}=7^{\frac{2}{5}}[/tex]
The answer is [tex]7^{\frac{2}{5}}[/tex].
Hence the simplified form of [tex]\frac{\sqrt[3]{7}}{\sqrt[5]{7}}=7^{\frac{2}{5}}[/tex].
