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

Here are the steps:



\[{(4x)}^{2}\times \frac{5}{4x}=40\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{4}^{2}{x}^{2}\times \frac{5}{4x}=40\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[16{x}^{2}\times \frac{5}{4x}=40\]

3
Simplify  \(16{x}^{2}\times \frac{5}{4x}\)  to  \(\frac{80{x}^{2}}{4x}\).
\[\frac{80{x}^{2}}{4x}=40\]

4
Take out the constants.
\[\frac{80}{4}\times \frac{{x}^{2}}{x}=40\]

5
Simplify  \(\frac{80}{4}\)  to  \(20\).
\[20\times \frac{{x}^{2}}{x}=40\]

6
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[20{x}^{2-1}=40\]

7
Simplify  \(2-1\)  to  \(1\).
\[20{x}^{1}=40\]

8
Use Rule of One: \({x}^{1}=x\).
\[20x=40\]

9
Divide both sides by \(20\).
\[x=\frac{40}{20}\]

10
Simplify  \(\frac{40}{20}\)  to  \(2\).
\[x=2\]

Done
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