Problem of the Week

Updated at Nov 19, 2018 1:37 PM

How would you solve the equation (4u)25+2=745\frac{{(4u)}^{2}}{5}+2=\frac{74}{5}?

Below is the solution.



(4u)25+2=745\frac{{(4u)}^{2}}{5}+2=\frac{74}{5}

1
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
42u25+2=745\frac{{4}^{2}{u}^{2}}{5}+2=\frac{74}{5}

2
Simplify  42{4}^{2}  to  1616.
16u25+2=745\frac{16{u}^{2}}{5}+2=\frac{74}{5}

3
Subtract 22 from both sides.
16u25=745−2\frac{16{u}^{2}}{5}=\frac{74}{5}-2

4
Simplify  745−2\frac{74}{5}-2  to  645\frac{64}{5}.
16u25=645\frac{16{u}^{2}}{5}=\frac{64}{5}

5
Multiply both sides by 55.
16u2=645×516{u}^{2}=\frac{64}{5}\times 5

6
Cancel 55.
16u2=6416{u}^{2}=64

7
Divide both sides by 1616.
u2=6416{u}^{2}=\frac{64}{16}

8
Simplify  6416\frac{64}{16}  to  44.
u2=4{u}^{2}=4

9
Take the square root of both sides.
u=±4u=\pm \sqrt{4}

10
Since 2×2=42\times 2=4, the square root of 44 is 22.
u=±2u=\pm 2

Done
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