Question

Evaluate (−23)×(−23)3 by using the Laws of Exponents

Answer 1

Given:

`\left(-(2)/(3)\right)* \left(-(2)/(3)\right)^3`

To find:

The value of given expression by using the Laws of Exponents.

Solution:

We have,

`\left(-(2)/(3)\right)* \left(-(2)/(3)\right)^3`

Using the Laws of Exponents, we get

`=\left(-(2)/(3)\right)^(1+3)`
`[\because a^ma^n=a^(m+n)]`

`=\left((-2)/(3)\right)^(4)`

`=((-2)^4)/((3)^4)`
`[\because \left((a)/(b)\right)^n=(a^n)/(b^n)]`

`=((-2)* (-2)* (-2)* (-2))/((3)* (3)* (3)* (3))`

`=(16)/(81)`

Therefore, the value of given expression is
`(16)/(81)`.