Problem of the Week

Updated at Jun 28, 2021 3:50 PM

This week's problem comes from the equation category.

How would you solve \(\frac{4}{5}{(4n)}^{2}=\frac{64}{5}\)?

Let's begin!



\[\frac{4}{5}{(4n)}^{2}=\frac{64}{5}\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{4}{5}\times {4}^{2}{n}^{2}=\frac{64}{5}\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[\frac{4}{5}\times 16{n}^{2}=\frac{64}{5}\]

3
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{4\times 16{n}^{2}}{5}=\frac{64}{5}\]

4
Simplify  \(4\times 16{n}^{2}\)  to  \(64{n}^{2}\).
\[\frac{64{n}^{2}}{5}=\frac{64}{5}\]

5
Multiply both sides by \(5\).
\[64{n}^{2}=\frac{64}{5}\times 5\]

6
Cancel \(5\).
\[64{n}^{2}=64\]

7
Divide both sides by \(64\).
\[{n}^{2}=1\]

8
Take the square root of both sides.
\[n=\pm \sqrt{1}\]

9
Simplify  \(\sqrt{1}\)  to  \(1\).
\[n=\pm 1\]

Done
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