Question

simplify the radical. assume that all variables represent positive real num\\(\sqrt4{a^{20}b^{12}}\\)select the correct choice below and, if necessary, fill in the answer box to\\(\boldsymbol{\text{a. } \sqrt4{a^{20}b^{12}} = \square}\\)\\(\text{b. the root is not a real number.}\\)help me solve this view an example get more hereview progress

Explanation:

Step1: Rewrite exponents for 4th root

Recall that $\sqrt[4]{x} = x^{\frac{1}{4}}$, so:
$$\sqrt[4]{a^{20}b^{12}} = (a^{20}b^{12})^{\frac{1}{4}}$$

Step2: Apply exponent power rule

Use $(x^m)^n = x^{m \cdot n}$ for each variable:
$$(a^{20})^{\frac{1}{4}} \cdot (b^{12})^{\frac{1}{4}} = a^{\frac{20}{4}} \cdot b^{\frac{12}{4}}$$

Step3: Simplify exponents

Calculate the simplified exponents:
$$a^{5} \cdot b^{3} = a^5b^3$$

Answer:

A. $\sqrt[4]{a^{20}b^{12}} = a^5b^3$