Chapter 7, Problem 20SGR

To determine

To Simplify: The expression $\frac{12y^{-4}}{3y^{-5}}$

Answer to Problem 20SGR

  $\frac{12y^{-4}}{3y^{-5}}=4y$

Explanation of Solution

Given information:

The expression $\frac{12y^{-4}}{3y^{-5}}$

Concept and Formula Used:

Rule of exponent.

  $\frac{a^m}{a^n}=a^{m-n}$

Calculation:

The given expression is

  $\begin{array}{l}\frac{12y^{-4}}{3y^{-5}}\\ \text{Using }\frac{a^m}{a^n}=a^{m-n}\\ \frac{12y^{-4}}{3y^{-5}}=\frac{12y^{-4-\left(-5\right)}}{3}\\ \text{Simplify}\\ \frac{12y^{-4}}{3y^{-5}}=4y^1\\ \frac{12y^{-4}}{3y^{-5}}=4y\end{array}$

Conclusion:

  $\frac{12y^{-4}}{3y^{-5}}=4y$