Explanation:
Given:
[tex]\sqrt[3]{16y^5z^{12}}[/tex]
Note: Rational exponents are another way of writing expressions with radicals. When you use rational exponents, you can apply the properties of exponents to simplify expressions. The Power Property for Exponents says that (am)n = am⋅n when m and n are whole numbers.
[tex]\begin{gathered} \sqrt[3]{16y^5z^{12}}=(16y^5z^{12})^{\frac{1}{3}} \\ =16^{\frac{1}{3}}\times y^{5\times\frac{1}{3}}\times z^{12\times\frac{1}{3}} \\ =16^{\frac{1}{3}}\times y^{\frac{5}{3}}\times z^4 \\ =2^{4\times\frac{1}{3}}\times y^{\frac{5}{3}}\times z^4 \\ =2^{\frac{4}{3}}\times y^{\frac{5}{3}}\times z^4 \\ =2^{\frac{4}{3}}y^{\frac{5}{3}}z^4 \end{gathered}[/tex]
