Question
QUESTION \( 18 \cdot 1 \) POINT Simplify: \( \left(a^{2}\right)^{7} \)
Ask by Weston Potter. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( a^{14} \)
Solution
Calculate or simplify the expression \( (a^2)^7 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(a^{2}\right)^{7}\)
- step1: Multiply the exponents:
\(a^{2\times 7}\)
- step2: Multiply the numbers:
\(a^{14}\)
The simplified form of \( \left(a^{2}\right)^{7} \) is \( a^{14} \).
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Simplify this solution Beyond the Answer
The expression \( \left(a^{2}\right)^{7} \) can be simplified by applying the power of a power rule in exponentiation, which states that \( (x^m)^n = x^{m \cdot n} \). Therefore, we multiply the exponents: \( 2 \cdot 7 = 14 \). So, the simplified expression is \( a^{14} \). For a fun little twist, think of it this way: if \( a \) was your favorite superhero, then \( a^2 \) is like giving them a sidekick! And when they team up and get boosted to the power of 7, they become an unstoppable force – hence, \( a^{14} \)! Super powers multiplied!
