# Problem of the Week

## Updated at Jan 2, 2023 2:24 PM

To get more practice in equation, we brought you this problem of the week:

How can we solve the equation $$6{(\frac{5}{4m})}^{2}=\frac{25}{24}$$?

Check out the solution below!

$6{(\frac{5}{4m})}^{2}=\frac{25}{24}$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$6\times \frac{{5}^{2}}{{(4m)}^{2}}=\frac{25}{24}$2 Simplify  $${5}^{2}$$  to  $$25$$.$6\times \frac{25}{{(4m)}^{2}}=\frac{25}{24}$3 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$6\times \frac{25}{{4}^{2}{m}^{2}}=\frac{25}{24}$4 Simplify  $${4}^{2}$$  to  $$16$$.$6\times \frac{25}{16{m}^{2}}=\frac{25}{24}$5 Simplify  $$6\times \frac{25}{16{m}^{2}}$$  to  $$\frac{150}{16{m}^{2}}$$.$\frac{150}{16{m}^{2}}=\frac{25}{24}$6 Simplify  $$\frac{150}{16{m}^{2}}$$  to  $$\frac{75}{8{m}^{2}}$$.$\frac{75}{8{m}^{2}}=\frac{25}{24}$7 Multiply both sides by $$8{m}^{2}$$.$75=\frac{25}{24}\times 8{m}^{2}$8 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$75=\frac{25\times 8{m}^{2}}{24}$9 Simplify  $$25\times 8{m}^{2}$$  to  $$200{m}^{2}$$.$75=\frac{200{m}^{2}}{24}$10 Simplify  $$\frac{200{m}^{2}}{24}$$  to  $$\frac{25{m}^{2}}{3}$$.$75=\frac{25{m}^{2}}{3}$11 Multiply both sides by $$3$$.$75\times 3=25{m}^{2}$12 Simplify  $$75\times 3$$  to  $$225$$.$225=25{m}^{2}$13 Divide both sides by $$25$$.$\frac{225}{25}={m}^{2}$14 Simplify  $$\frac{225}{25}$$  to  $$9$$.$9={m}^{2}$15 Take the square root of both sides.$\pm \sqrt{9}=m$16 Since $$3\times 3=9$$, the square root of $$9$$ is $$3$$.$\pm 3=m$17 Switch sides.$m=\pm 3$Donem=3,-3