Problem of the Week

Updated at Sep 28, 2026 10:23 AM

This week we have another equation problem:

How would you solve \(\frac{{(q-3)}^{2}(q-3)}{5}=\frac{8}{5}\)?

Let's start!



\[\frac{{(q-3)}^{2}(q-3)}{5}=\frac{8}{5}\]

1
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{(q-3)}^{3}}{5}=\frac{8}{5}\]

2
Multiply both sides by \(5\).
\[{(q-3)}^{3}=\frac{8}{5}\times 5\]

3
Cancel \(5\).
\[{(q-3)}^{3}=8\]

4
Take the cube root of both sides.
\[q-3=\sqrt[3]{8}\]

5
Calculate.
\[q-3=2\]

6
Add \(3\) to both sides.
\[q=2+3\]

7
Simplify  \(2+3\)  to  \(5\).
\[q=5\]

Done
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