Question

question
select the expression that is equivalent to (sqrt5{3} cdot sqrt5{3}).

answer
(\bigcirc) (3^{25}) (\bigcirc) (3^{\frac{2}{5}})
(\bigcirc) (3^{\frac{5}{2}}) (\bigcirc) (3^{\frac{1}{25}})

Explanation:

Step1: Convert root to exponent

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

Step2: Multiply the two expressions

$3^{\frac{1}{5}} \cdot 3^{\frac{1}{5}} = 3^{\frac{1}{5}+\frac{1}{5}}$

Step3: Add the exponents

$3^{\frac{1}{5}+\frac{1}{5}} = 3^{\frac{2}{5}}$

Answer:

$\boldsymbol{3^{\frac{2}{5}}}$ (the top-right option)