Question

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

$\left(\frac{12}{2}\right)\left(\frac{x}{y^5}\right)\left(\frac{y^4}{x^4}\right)$

Short answer

The final expression is $\frac{6}{x^3{y}^4}$.

Step-by-step solution

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

$\frac{a^m}{a^n}=\frac{1}{a^{n-m}}$

Where,$a$ is any non-zero real number and $n>m$.

Step 3. Simplify the expression 122xy5y4x4.

Use the property of power of a power rule.

$$\begin{gathered} \left(\frac{12}{2}\right)\left(\frac{x}{y^5}\right)\left(\frac{y^4}{x^4}\right)=6\left(\frac{x}{x^4}\right)\left(\frac{y^4}{y^5}\right) \\ =6\left(\frac{1}{x^{4-1}}\right)\left(\frac{1}{y^{5-1}}\right) \\ =6\left(\frac{1}{x^3}\right)\left(\frac{1}{y^4}\right) \\ =\frac{6}{x^3{y}^4} \end{gathered}$$

Hence,$\left(\frac{12}{2}\right)\left(\frac{x}{y^5}\right)\left(\frac{y^4}{x^4}\right)=\frac{6}{x^3{y}^4}$

Therefore the final expression is $\frac{6}{x^3{y}^4}$.