# Problem of the Week

## Updated at Feb 15, 2021 1:23 PM

This week we have another equation problem:

How would you solve $$\frac{{(\frac{4x}{5})}^{2}}{5}=\frac{16}{5}$$?

Let's start!

$\frac{{(\frac{4x}{5})}^{2}}{5}=\frac{16}{5}$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$\frac{\frac{{(4x)}^{2}}{{5}^{2}}}{5}=\frac{16}{5}$2 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$\frac{\frac{{4}^{2}{x}^{2}}{{5}^{2}}}{5}=\frac{16}{5}$3 Simplify  $${4}^{2}$$  to  $$16$$.$\frac{\frac{16{x}^{2}}{{5}^{2}}}{5}=\frac{16}{5}$4 Simplify  $${5}^{2}$$  to  $$25$$.$\frac{\frac{16{x}^{2}}{25}}{5}=\frac{16}{5}$5 Simplify  $$\frac{\frac{16{x}^{2}}{25}}{5}$$  to  $$\frac{16{x}^{2}}{25\times 5}$$.$\frac{16{x}^{2}}{25\times 5}=\frac{16}{5}$6 Simplify  $$25\times 5$$  to  $$125$$.$\frac{16{x}^{2}}{125}=\frac{16}{5}$7 Multiply both sides by $$125$$.$16{x}^{2}=\frac{16}{5}\times 125$8 Use this rule: $$\frac{a}{b} \times c=\frac{ac}{b}$$.$16{x}^{2}=\frac{16\times 125}{5}$9 Simplify  $$16\times 125$$  to  $$2000$$.$16{x}^{2}=\frac{2000}{5}$10 Simplify  $$\frac{2000}{5}$$  to  $$400$$.$16{x}^{2}=400$11 Divide both sides by $$16$$.${x}^{2}=\frac{400}{16}$12 Simplify  $$\frac{400}{16}$$  to  $$25$$.${x}^{2}=25$13 Take the square root of both sides.$x=\pm \sqrt{25}$14 Since $$5\times 5=25$$, the square root of $$25$$ is $$5$$.$x=\pm 5$Done x=5,-5