Question

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Part 1
Find the real solutions to the equation.
96=3q^5

Answer 1

To solve the equation \( 96 = 3q^5 \), we can begin by isolating \( q^5 \).

1. Divide both sides by 3:
\[
q^5 = \frac{96}{3} = 32
\]

2. Now, we need to take the fifth root of both sides to find \( q \):
\[
q = \sqrt[5]{32}
\]

3. Recognizing that \( 32 \) is \( 2^5 \), we can simplify:
\[
q = \sqrt[5]{2^5} = 2
\]

Thus, the real solution to the equation \( 96 = 3q^5 \) is:
\[
\boxed{2}
\]