Question

I need help asap !!​

Answer 1

Answer:

Solving the expression  $\frac{\sqrt[3]{7} }{\sqrt[5]{7} }$ we get $\mathbf{7^{\frac{2}{15}}}$

Option D is correct option.

Step-by-step explanation:

We need to solve the expression: $\frac{\sqrt[3]{7} }{\sqrt[5]{7} }$

We know that

$\sqrt[3]{x}=x^{\frac{1}{3}$ and $\sqrt[5]{x}=x^{\frac{1}{5}$

Using above rule:

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

Now, we know the exponent rule if bases are same and divided then exponents are subtracted i.e:  $\frac{a^m}{a^n}=a^{m-n}$

Using the exponent rule

$=7^{\frac{1}{3}-\frac{1}{5} }\\Simplifying\:exponents\\=7^{\frac{5-3}{15}}\\=7^{\frac{1*5-1*3}{15}}\\=7^{\frac{2}{15}}$

So, solving the expression  $\frac{\sqrt[3]{7} }{\sqrt[5]{7} }$ we get $\mathbf{7^{\frac{2}{15}}}$

Option D is correct option.