Problem of the Week

Updated at Feb 15, 2021 1:23 PM

This week we have another equation problem:

How would you solve (4x5)25=165\frac{{(\frac{4x}{5})}^{2}}{5}=\frac{16}{5}?

Let's start!



(4x5)25=165\frac{{(\frac{4x}{5})}^{2}}{5}=\frac{16}{5}

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
(4x)2525=165\frac{\frac{{(4x)}^{2}}{{5}^{2}}}{5}=\frac{16}{5}

2
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
42x2525=165\frac{\frac{{4}^{2}{x}^{2}}{{5}^{2}}}{5}=\frac{16}{5}

3
Simplify  42{4}^{2}  to  1616.
16x2525=165\frac{\frac{16{x}^{2}}{{5}^{2}}}{5}=\frac{16}{5}

4
Simplify  52{5}^{2}  to  2525.
16x2255=165\frac{\frac{16{x}^{2}}{25}}{5}=\frac{16}{5}

5
Simplify  16x2255\frac{\frac{16{x}^{2}}{25}}{5}  to  16x225×5\frac{16{x}^{2}}{25\times 5}.
16x225×5=165\frac{16{x}^{2}}{25\times 5}=\frac{16}{5}

6
Simplify  25×525\times 5  to  125125.
16x2125=165\frac{16{x}^{2}}{125}=\frac{16}{5}

7
Multiply both sides by 125125.
16x2=165×12516{x}^{2}=\frac{16}{5}\times 125

8
Use this rule: ab×c=acb\frac{a}{b} \times c=\frac{ac}{b}.
16x2=16×125516{x}^{2}=\frac{16\times 125}{5}

9
Simplify  16×12516\times 125  to  20002000.
16x2=2000516{x}^{2}=\frac{2000}{5}

10
Simplify  20005\frac{2000}{5}  to  400400.
16x2=40016{x}^{2}=400

11
Divide both sides by 1616.
x2=40016{x}^{2}=\frac{400}{16}

12
Simplify  40016\frac{400}{16}  to  2525.
x2=25{x}^{2}=25

13
Take the square root of both sides.
x=±25x=\pm \sqrt{25}

14
Since 5×5=255\times 5=25, the square root of 2525 is 55.
x=±5x=\pm 5

Done
Cymath foriOSAndroid