# Problem of the Week

## Updated at Aug 24, 2020 11:12 AM

How can we solve the equation $$\frac{4x}{5{(\frac{x}{5})}^{2}}=5$$?

Below is the solution.

$\frac{4x}{5{(\frac{x}{5})}^{2}}=5$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$\frac{4x}{5\times \frac{{x}^{2}}{{5}^{2}}}=5$2 Simplify  $${5}^{2}$$  to  $$25$$.$\frac{4x}{5\times \frac{{x}^{2}}{25}}=5$3 Simplify  $$5\times \frac{{x}^{2}}{25}$$  to  $$\frac{{x}^{2}}{5}$$.$\frac{4x}{\frac{{x}^{2}}{5}}=5$4 Invert and multiply.$4x\times \frac{5}{{x}^{2}}=5$5 Simplify  $$4x\times \frac{5}{{x}^{2}}$$  to  $$\frac{20x}{{x}^{2}}$$.$\frac{20x}{{x}^{2}}=5$6 Use Quotient Rule: $$\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}$$.$20{x}^{1-2}=5$7 Simplify  $$1-2$$  to  $$-1$$.$20{x}^{-1}=5$8 Use Negative Power Rule: $${x}^{-a}=\frac{1}{{x}^{a}}$$.$20\times \frac{1}{x}=5$9 Simplify  $$20\times \frac{1}{x}$$  to  $$\frac{20}{x}$$.$\frac{20}{x}=5$10 Multiply both sides by $$x$$.$20=5x$11 Divide both sides by $$5$$.$\frac{20}{5}=x$12 Simplify  $$\frac{20}{5}$$  to  $$4$$.$4=x$13 Switch sides.$x=4$Done x=4