Question

question
select the expression that is equivalent to (sqrt6{3^{5}} cdot sqrt{3}).

answer
(\bigcirc) (3^{\frac{4}{3}}) (\bigcirc) (3^{\frac{12}{5}})
(\bigcirc) (3^{\frac{5}{12}}) (\bigcirc) (3^{\frac{3}{4}})

Explanation:

Step1: Convert roots to exponents

$\sqrt[6]{3^5} = 3^{\frac{5}{6}}$, $\sqrt{3} = 3^{\frac{1}{2}}$

Step2: Add exponents (same base)

$3^{\frac{5}{6} + \frac{1}{2}} = 3^{\frac{5}{6} + \frac{3}{6}} = 3^{\frac{8}{6}}$

Step3: Simplify the exponent

$3^{\frac{8}{6}} = 3^{\frac{4}{3}}$

Answer:

$3^{\frac{4}{3}}$