Q24. - Algebra 1

Question

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

$\frac{-15x^7{y}^8{z}^4}{-45x^3{y}^5{z}^3}$

Step-by-Step Solution

Answer

The final expression is $\frac{x^4{y}^{3}z}{3}$.

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 − 15 x 7 y 8 z 4 − 45 x 3 y 5 z 3 .

Use the property of quotient of power rule.

$$\begin{gathered} \frac{-15x^7{y}^8{z}^4}{-45x^3{y}^5{z}^3}=\left(\frac{-15}{-45}\right)\left(\frac{x^7}{x^3}\right)\left(\frac{y^8}{y^5}\right)\left(\frac{z^4}{z^3}\right) \\ =\left(\frac{1}{3}\right)\left(x^{7-3}\right)\left(y^{8-5}\right)\left(z^{4-3}\right) \\ =\left(\frac{1}{3}\right)\left(x^4\right)\left(y^3\right)\left(z^1\right) \\ =\frac{x^4{y}^{3}z}{3} \end{gathered}$$

Hence, $\frac{-15x^7{y}^8{z}^4}{-45x^3{y}^5{z}^3}=\frac{x^4{y}^{3}z}{3}$

Therefore the final expression is $\frac{x^4{y}^{3}z}{3}$.