Question

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

Answer 1

Given:

$\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3$

To find:

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

Solution:

We have,

$\left(-\dfrac{2}{3}\right)\times \left(-\dfrac{2}{3}\right)^3$

Using the Laws of Exponents, we get

$=\left(-\dfrac{2}{3}\right)^{1+3}$      $[\because a^ma^n=a^{m+n}]$

$=\left(\dfrac{-2}{3}\right)^{4}$

$=\dfrac{(-2)^4}{(3)^4}$      $[\because \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}]$

$=\dfrac{(-2)\times (-2)\times (-2)\times (-2)}{(3)\times (3)\times (3)\times (3)}$

$=\dfrac{16}{81}$

Therefore, the value of given expression is $\dfrac{16}{81}$.