Question
8 Multiple Choice 0.5 points Simply the expression: \( \left(\frac{8 a^{2} b^{4} c^{2}}{4 a^{3} b^{3} c^{2}}\right)^{0} \) a) 1 b) 2 abc c) 0 d) \( \frac{2 b}{a} \)
Ask by Wade Reed. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is 1.
Solution
The expression given is:
\[
\left(\frac{8 a^{2} b^{4} c^{2}}{4 a^{3} b^{3} c^{2}}\right)^0
\]
Any non-zero base raised to the power of 0 is equal to 1. Therefore:
\[
\left(\frac{8 a^{2} b^{4} c^{2}}{4 a^{3} b^{3} c^{2}}\right)^0 = 1
\]
**Answer:**
a) 1
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Simplify this solution Extra Insights
No matter what the expression inside the parentheses is, any non-zero base raised to the power of zero is always equal to 1. This rule applies to any expression, so you can confidently select option a) 1! And remember, this zero exponent rule is like magic for simplifying expressions in algebra—it helps you wave away complicated parts and still get a simple solution! Just keep in mind, zero raised to the power of zero (0^0) is a whole different story and can be a bit controversial!
