Chapter 6, Problem 1CR

To determine

To simplify the expression

  $y^3\cdot y^{-5}$

Write the answer in positive exponents.

Answer to Problem 1CR

  $\frac{1}{y^2}$

Explanation of Solution

Given:

  $y^3\cdot y^{-5}$

Concept Used:

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

  ${\left(ab\right)}^m=a^m{b}^m$

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

  $a^{-m}=\frac{1}{a^m}$

Calculation:

In order to simplify the expression

  $y^3\cdot y^{-5}$

Apply the above mentioned properties and solve it as,

  $\begin{array}{c}{y}^3\cdot y^{-5}=y^3\left(\frac{1}{y^5}\right)\\ =\frac{y^3}{y^5}\\ =\frac{y\times y\times y}{y\times y\times y\times y\times y}\\ =\frac{1}{y\times y}\\ =\frac{1}{y^2}\end{array}$

Thus, the given expression becomes,

  $\frac{1}{y^2}$