Answer:
Solving the expression [tex]\frac{\sqrt[3]{7} }{\sqrt[5]{7} }[/tex] we get [tex]\mathbf{7^{\frac{2}{15}}}[/tex]
Option D is correct option.
Step-by-step explanation:
We need to solve the expression: [tex]\frac{\sqrt[3]{7} }{\sqrt[5]{7} }[/tex]
We know that
[tex]\sqrt[3]{x}=x^{\frac{1}{3}[/tex] and [tex]\sqrt[5]{x}=x^{\frac{1}{5}[/tex]
Using above rule:
[tex]\frac{\sqrt[3]{7} }{\sqrt[5]{7} }\\=\frac{7^{\frac{1}{3}}}{7^{\frac{1}{5}}}[/tex]
Now, we know the exponent rule if bases are same and divided then exponents are subtracted i.e: [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
Using the exponent rule
[tex]=7^{\frac{1}{3}-\frac{1}{5} }\\Simplifying\:exponents\\=7^{\frac{5-3}{15}}\\=7^{\frac{1*5-1*3}{15}}\\=7^{\frac{2}{15}}[/tex]
So, solving the expression [tex]\frac{\sqrt[3]{7} }{\sqrt[5]{7} }[/tex] we get [tex]\mathbf{7^{\frac{2}{15}}}[/tex]
Option D is correct option.
