Question

simplify the expression shown below.
$6^{\frac{1}{3}} \cdot 36^{\frac{1}{3}}$

$6^{\frac{1}{3}} \cdot 36^{\frac{1}{3}} = \square$
(simplify your answer, including any radicals. use integers

Explanation:

Step1: Rewrite 36 as power of 6

$36 = 6^2$, so $36^{\frac{1}{3}} = (6^2)^{\frac{1}{3}}$

Step2: Simplify the exponent

$(6^2)^{\frac{1}{3}} = 6^{\frac{2}{3}}$

Step3: Combine the terms

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

Step4: Add the exponents

$\frac{1}{3}+\frac{2}{3} = 1$, so $6^{1}=6$

Answer:

$6$