Chapter 6, Problem 3CR

To determine

To simplify the expression

  ${\left(x^0{y}^2\right)}^3$

Write the answer in positive exponents.

Answer to Problem 3CR

  $y^6$

Explanation of Solution

Given:

  ${\left(x^0{y}^2\right)}^3$

Concept Used:

Let a and b be real numbers, and let m be an integer, then

  ${\left(ab\right)}^m=a^m{b}^m$

  ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m},b\ne 0$

  $a^{-m}=\frac{1}{a^m}$

  $a^0=1$

Calculation:

In order to simplify the expression

  ${\left(x^0{y}^2\right)}^3$

Apply the above mentioned properties and solve it as,

  $\begin{array}{c}{\left(x^0{y}^2\right)}^3={\left(x^0\right)}^3{\left(y^2\right)}^3\\ ={\left(1\right)}^3{\left(y\right)}^{2\times 3}\\ =1\left(y^6\right)\\ =y^6\end{array}$

Thus, the given expression becomes,

  $y^6$