Question
3.) \( \left(a^{-2}\right)\left(-3 a^{0}\right) \)
Ask by Carroll Christensen. in South Africa
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is –3a⁻² or –3/(a²).
Solution
We start with the expression:
(a^(–2)) · (–3 a^(0))
Step 1: Recall that a^(0) = 1. Thus, the expression becomes:
a^(–2) · (–3 · 1) = –3 · a^(–2)
Step 2: Write the answer. The simplified expression is:
–3a^(–2)
Alternatively, since a^(–2) = 1/(a²), the expression can also be written as:
–3/(a²)
Thus, the final answer is:
–3a^(–2) or –3/(a²)
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Simplify this solution Beyond the Answer
Let’s break it down! First, recall that anything raised to the power of zero equals one, so \( a^{0} = 1 \). Then the expression simplifies to \( \left(a^{-2}\right)(-3 \cdot 1) = -3a^{-2} \). Remember, \( a^{-2} \) can also be rewritten as \( \frac{1}{a^{2}} \), so you could express the final result as \( -\frac{3}{a^{2}} \) if that looks better to you! Now, whenever you're doing math involving exponents, keep an eye on those negative powers—they're just a way of saying "divide by." But a common mistake is forgetting that \( a^{0} = 1 \); don’t let it trip you up! It's like finding a hidden treasure in your math toolkit!
