Question

Use the laws of exponents to simplify expressions with rational exponents Number 572

Answer 1

Given,

The expression is:

$\begin{gathered} a)(x^{12})^{\frac{2}{3}} \\ b)(y^{20})^{\frac{2}{5}} \\ c)(z^{16})^{\frac{1}{16}} \end{gathered}$

Simplifying the expressions,

$\begin{gathered} a)(x^{12})^{\frac{2}{3}}=x^{12\times\frac{2}{3}} \\ =x^{4\times2} \\ =x^8 \end{gathered}$

The simplified expression is x^8.

$\begin{gathered} b)(y^{20})^{\frac{2}{5}}=y^{20\times\frac{2}{5}} \\ =y^{4\times2} \\ =y^8 \end{gathered}$

The simplified expression is y^8.

$\begin{gathered} c)(z^{16})^{\frac{1}{16}}=z^{16\times\frac{1}{16}} \\ =z \end{gathered}$

Hence, the simplified value is z.