Q22. - Algebra 1

Question

Simplify the given expression. Assume that no denominator equals zero.

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

Step-by-Step Solution

Answer

The final expression is $4y$.

Step 1. Define an expression.

A mathematical expression is a combinations of numbers and variables ordered with mathematical operations.

Step 2. Define quotient of power rule.

The quotient of power rule is given by,

$\frac{a^m}{a^n}=a^{m-n}$

Where, $a$ is any non-zero real number.

Step 3. Simplify the expression 12 y − 4 3 y − 5 .

Use the property of quotient of power rule.

$$\begin{gathered} \frac{12y^{-4}}{3y^{-5}}=\left(\frac{12}{3}\right)\left(\frac{y^{-4}}{y^{-5}}\right) \\ =\left(4\right)\left(y^{-4-\left(-5\right)}\right) \\ =4\left(y^{-4+5}\right) \\ =4\left(y^1\right) \\ =4y \end{gathered}$$

Hence, $\frac{12y^{-4}}{3y^{-5}}=4y$

Therefore the final expression is $4y$.