Question

Write (8a^3)^ -2/3 in simplest form

Answer 1

$(8^{3})^{\frac{-2}{3}}\\ \frac{1}{(8a^{3})^{\frac{2}{3}}}\\ \frac{1}{ \sqrt[3]{(8a^{3})^2}}\\ \frac{1}{ \sqrt[3]{(64a^{6})}}\\\\ \frac{1}{ 4a^{2}}}$

Answer 2

Answer:

$(8a^3)^{-\frac{2}{3}}=\frac{1}{4a^2}$

Step-by-step explanation:

Given : Expression $(8a^3)^{-\frac{2}{3}}$

To find : The simplest form of the expression

Solution :

We solve the expression step by step :

Step 1- Write the expression

$(8a^3)^{-\frac{2}{3}}$

Step 2- Taking the power in denominator

$=\frac{1}{(8a^3)^{\frac{2}{3}}}$

Step 3- Taking cube outside

$=\frac{1}{(2a)^{\frac{2\times3}{3}}}$

Step 4- 3 will cancel out

$=\frac{1}{(2a)^2}$

Step 5- Solving the squaring

$=\frac{1}{4a^2}$

Therefore, The simplest form of given expression is

$(8a^3)^{-\frac{2}{3}}=\frac{1}{4a^2}$