Problem of the Week

Updated at Dec 2, 2024 8:26 AM

For this week we've brought you this equation problem.

How would you solve (4x)2×54x=40{(4x)}^{2}\times \frac{5}{4x}=40?

Here are the steps:



(4x)2×54x=40{(4x)}^{2}\times \frac{5}{4x}=40

1
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
42x2×54x=40{4}^{2}{x}^{2}\times \frac{5}{4x}=40

2
Simplify  42{4}^{2}  to  1616.
16x2×54x=4016{x}^{2}\times \frac{5}{4x}=40

3
Simplify  16x2×54x16{x}^{2}\times \frac{5}{4x}  to  80x24x\frac{80{x}^{2}}{4x}.
80x24x=40\frac{80{x}^{2}}{4x}=40

4
Take out the constants.
804×x2x=40\frac{80}{4}\times \frac{{x}^{2}}{x}=40

5
Simplify  804\frac{80}{4}  to  2020.
20×x2x=4020\times \frac{{x}^{2}}{x}=40

6
Use Quotient Rule: xaxb=xa−b\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}.
20x2−1=4020{x}^{2-1}=40

7
Simplify  2−12-1  to  11.
20x1=4020{x}^{1}=40

8
Use Rule of One: x1=x{x}^{1}=x.
20x=4020x=40

9
Divide both sides by 2020.
x=4020x=\frac{40}{20}

10
Simplify  4020\frac{40}{20}  to  22.
x=2x=2

Done
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