Question

1/3 root 4^-5. solve using laws of exponents with correct steps. plz answer fast​

Answer 1

Answer:

4

$\sqrt{16}$

Answer 2

The simpler form of the expression $\frac{1}{\sqrt[3]{4^{-5}} }$ is $4\sqrt[3]{16}$.

Given,

The expression: $\frac{1}{\sqrt[3]{4^{-5}} }$.

To Find,

We need to find a simpler form of the expression using the laws of exponents.

Solution,

The method of finding the simpler form of the expression is as follows -

We will try to simplify the expression by using the laws of exponents.

$\frac{1}{\sqrt[3]{4^{-5}} }=\frac{1}{4^{-\frac{5}{3} }} }$[ Since $\sqrt[n]{x} =x^{\frac{1}{n} }$]

$=4^{\frac{5}{3} }$ [Since $\frac{1}{x^{-n}}=x^{n}$]

$=(4^{3+2})^{\frac{1}{3} }=(4^{3}*4^{2})^{\frac{1}{3} }$ [Since $a^{m+n}=a^m*a^n$]

$=(4^3)^{\frac{1}{3} }*(4^2)^{\frac{1}{3} }$ [Since $(ab)^m=a^m*b^m$]

$=4*16^{\frac{1}{3} }=4\sqrt[3]{16}$.

Hence, the simpler form of the expression $\frac{1}{\sqrt[3]{4^{-5}} }$ is $4\sqrt[3]{16}$.

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