Question

Simplify each expression. Assume that no denominator equals 0.

$\frac{\mathbf{2}x{y}^{-\mathbf{7}}}{\mathbf{8}x}$

Short answer

The expression$\frac{2x{y}^{-7}}{8x}$ can be simplified to $\frac{1}{4}{y}^{-\mathbf{7}}$.

Step-by-step solution

Step 1. Group powers with same base.

Group powers with same base in given expression.

$\left(\frac{2}{8}\right)\left(\frac{x}{x}\right)y^{-7}$

Step 2. Write quotient of powers rule.

For any nonzero number x and any integers m and n, $\frac{x^m}{x^n}=x^{m-n}$.

Step 3. Apply quotient of powers rule to given expression.

Apply quotient of powers rule to step 1.

$\frac{2}{8}{x}^{1-1}{y}^{-7}$

Step 4. Simplify the expression.

Simplify the expression obtained in step 3.

$\frac{1}{4}{x}^0{y}^{-7}=\frac{1}{4}{y}^{-7}$

Therefore,$\frac{2x{y}^{-7}}{8x}$ can be simplified to $\frac{1}{4}{y}^{-7}$.