Problem of the Week

Updated at Feb 17, 2025 11:31 AM

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

How would you solve the equation \({(\frac{{(u+2)}^{2}}{6})}^{2}=\frac{64}{9}\)?

Here are the steps:



\[{(\frac{{(u+2)}^{2}}{6})}^{2}=\frac{64}{9}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{{({(u+2)}^{2})}^{2}}{{6}^{2}}=\frac{64}{9}\]

2
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{(u+2)}^{4}}{{6}^{2}}=\frac{64}{9}\]

3
Simplify  \({6}^{2}\)  to  \(36\).
\[\frac{{(u+2)}^{4}}{36}=\frac{64}{9}\]

4
Multiply both sides by \(36\).
\[{(u+2)}^{4}=\frac{64}{9}\times 36\]

5
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[{(u+2)}^{4}=\frac{64\times 36}{9}\]

6
Simplify  \(64\times 36\)  to  \(2304\).
\[{(u+2)}^{4}=\frac{2304}{9}\]

7
Simplify  \(\frac{2304}{9}\)  to  \(256\).
\[{(u+2)}^{4}=256\]

8
Take the \(4\)th root of both sides.
\[u+2=\pm \sqrt[4]{256}\]

9
Calculate.
\[u+2=\pm 4\]

10
Break down the problem into these 2 equations.
\[u+2=4\]
\[u+2=-4\]

11
Solve the 1st equation: \(u+2=4\).
\[u=2\]

12
Solve the 2nd equation: \(u+2=-4\).
\[u=-6\]

13
Collect all solutions.
\[u=2,-6\]

Done
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