Martin Marshall
10/18/2023 · Middle School
Note: We can only use the product rule when we multiply expressions together. Simplify. \( 3^{4}+3^{2}=\square \)
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Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( 3^{4} + 3^{2} \), we can factor out the common term \( 3^{2} \).
1. Rewrite \( 3^{4} \) as \( (3^{2})^{2} \):
\[
3^{4} = 3^{2} \cdot 3^{2}
\]
2. Now, we can factor \( 3^{2} \) out of the expression:
\[
3^{4} + 3^{2} = 3^{2} \cdot 3^{2} + 3^{2} \cdot 1 = 3^{2}(3^{2} + 1)
\]
3. Now, calculate \( 3^{2} \):
\[
3^{2} = 9
\]
4. Substitute \( 3^{2} \) back into the expression:
\[
3^{2}(3^{2} + 1) = 9(9 + 1) = 9 \cdot 10 = 90
\]
Thus, the simplified expression is:
\[
3^{4} + 3^{2} = 90
\]
So, the answer is \( \boxed{90} \).
Quick Answer
\( 3^{4} + 3^{2} = 90 \)
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