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 45(4n)2=645\frac{4}{5}{(4n)}^{2}=\frac{64}{5}?

Let's begin!



45(4n)2=645\frac{4}{5}{(4n)}^{2}=\frac{64}{5}

1
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
45×42n2=645\frac{4}{5}\times {4}^{2}{n}^{2}=\frac{64}{5}

2
Simplify  42{4}^{2}  to  1616.
45×16n2=645\frac{4}{5}\times 16{n}^{2}=\frac{64}{5}

3
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
4×16n25=645\frac{4\times 16{n}^{2}}{5}=\frac{64}{5}

4
Simplify  4×16n24\times 16{n}^{2}  to  64n264{n}^{2}.
64n25=645\frac{64{n}^{2}}{5}=\frac{64}{5}

5
Multiply both sides by 55.
64n2=645×564{n}^{2}=\frac{64}{5}\times 5

6
Cancel 55.
64n2=6464{n}^{2}=64

7
Divide both sides by 6464.
n2=1{n}^{2}=1

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

9
Simplify  1\sqrt{1}  to  11.
n=±1n=\pm 1

Done
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