# Problem of the Week

## Updated at Nov 2, 2020 3:42 PM

How can we solve the equation $$5\times \frac{6}{{(4x)}^{2}}=\frac{3}{40}$$?

Below is the solution.

$5\times \frac{6}{{(4x)}^{2}}=\frac{3}{40}$

 1 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$5\times \frac{6}{{4}^{2}{x}^{2}}=\frac{3}{40}$2 Simplify  $${4}^{2}$$  to  $$16$$.$5\times \frac{6}{16{x}^{2}}=\frac{3}{40}$3 Simplify  $$5\times \frac{6}{16{x}^{2}}$$  to  $$\frac{30}{16{x}^{2}}$$.$\frac{30}{16{x}^{2}}=\frac{3}{40}$4 Simplify  $$\frac{30}{16{x}^{2}}$$  to  $$\frac{15}{8{x}^{2}}$$.$\frac{15}{8{x}^{2}}=\frac{3}{40}$5 Multiply both sides by $$8{x}^{2}$$.$15=\frac{3}{40}\times 8{x}^{2}$6 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$15=\frac{3\times 8{x}^{2}}{40}$7 Simplify  $$3\times 8{x}^{2}$$  to  $$24{x}^{2}$$.$15=\frac{24{x}^{2}}{40}$8 Simplify  $$\frac{24{x}^{2}}{40}$$  to  $$\frac{3{x}^{2}}{5}$$.$15=\frac{3{x}^{2}}{5}$9 Multiply both sides by $$5$$.$15\times 5=3{x}^{2}$10 Simplify  $$15\times 5$$  to  $$75$$.$75=3{x}^{2}$11 Divide both sides by $$3$$.$\frac{75}{3}={x}^{2}$12 Simplify  $$\frac{75}{3}$$  to  $$25$$.$25={x}^{2}$13 Take the square root of both sides.$\pm \sqrt{25}=x$14 Since $$5\times 5=25$$, the square root of $$25$$ is $$5$$.$\pm 5=x$15 Switch sides.$x=\pm 5$Done x=5,-5