Question
c. \( \left(\frac{R^{4}}{2 R^{2}}\right)^{3} \)
Ask by Bush Spencer. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{R^{6}}{8} \).
Solution
Calculate or simplify the expression \( (R^{4}/(2*R^{2}))^{3} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\frac{R^{4}}{2R^{2}}\right)^{3}\)
- step1: Divide the terms:
\(\left(\frac{R^{2}}{2}\right)^{3}\)
- step2: Rewrite the expression:
\(\frac{\left(R^{2}\right)^{3}}{2^{3}}\)
- step3: Evaluate the power:
\(\frac{R^{6}}{8}\)
The simplified form of \( \left(\frac{R^{4}}{2 R^{2}}\right)^{3} \) is \( \frac{R^{6}}{8} \).
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Simplify this solution Bonus Knowledge
First, let's simplify the expression \( \left(\frac{R^{4}}{2 R^{2}}\right)^{3} \). We can break it down step by step. First, simplify the fraction inside the parentheses: \[ \frac{R^{4}}{2 R^{2}} = \frac{R^{4}}{R^{2}} \cdot \frac{1}{2} = \frac{R^{2}}{2}. \] Now, we can raise this simplified fraction to the power of 3: \[ \left(\frac{R^{2}}{2}\right)^{3} = \frac{(R^{2})^{3}}{2^{3}} = \frac{R^{6}}{8}. \] So, the final simplified form of the original expression is \[ \frac{R^{6}}{8}. \] This means we took a complicated fraction, broke it down, and found a neat little result! Perfect for showing off your algebra skills!
