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))^{(2)/(3)} \\ b)(y^(20))^{(2)/(5)} \\ c)(z^(16))^{(1)/(16)} \end{gathered}`

Simplifying the expressions,

`\begin{gathered} a)(x^(12))^{(2)/(3)}=x^{12*(2)/(3)} \\ =x^(4*2) \\ =x^8 \end{gathered}`

The simplified expression is x^8.

`\begin{gathered} b)(y^(20))^{(2)/(5)}=y^{20*(2)/(5)} \\ =y^(4*2) \\ =y^8 \end{gathered}`

The simplified expression is y^8.

`\begin{gathered} c)(z^(16))^{(1)/(16)}=z^{16*(1)/(16)} \\ =z \end{gathered}`

Hence, the simplified value is z.