select the expression that is equivalent to $sqrt5{7^2} cdot sqrt5{7}$. \nanswer\n$\bigcirc$…

select the expression that is equivalent to $sqrt5{7^2} cdot sqrt5{7}$. \nanswer\n$\bigcirc$ $49^{\frac{3}{5}}$\n$\bigcirc$ $49^{\frac{2}{25}}$\n$\bigcirc$ $7^{\frac{2}{25}}$\n$\bigcirc$ $7^{\frac{3}{5}}$

select the expression that is equivalent to $sqrt5{7^2} cdot sqrt5{7}$. \nanswer\n$\bigcirc$ $49^{\frac{3}{5}}$\n$\bigcirc$ $49^{\frac{2}{25}}$\n$\bigcirc$ $7^{\frac{2}{25}}$\n$\bigcirc$ $7^{\frac{3}{5}}$

Answer

Explanation:

Step1: Convert roots to exponents

Recall that $\sqrt[n]{a^m}=a^{\frac{m}{n}}$, so: $\sqrt[5]{7^2}=7^{\frac{2}{5}}$, $\sqrt[5]{7}=7^{\frac{1}{5}}$

Step2: Multiply like bases, add exponents

When multiplying $a^x \cdot a^y=a^{x+y}$, so: $7^{\frac{2}{5}} \cdot 7^{\frac{1}{5}}=7^{\frac{2}{5}+\frac{1}{5}}$

Step3: Simplify the exponent

$\frac{2}{5}+\frac{1}{5}=\frac{3}{5}$, so the expression becomes $7^{\frac{3}{5}}$

Answer:

D. $7^{\frac{3}{5}}$