Question
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Answer
\( \frac{125}{v^{6}} \)
Solution
Calculate or simplify the expression \( (5v^{-2})^{3} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(5v^{-2}\right)^{3}\)
- step1: Use the properties of exponents:
\(5^{3}\left(v^{-2}\right)^{3}\)
- step2: Evaluate the power:
\(125v^{-6}\)
- step3: Simplify:
\(\frac{125}{v^{6}}\)
The simplified form of \( \left(5 v^{-2}\right)^{3} \) is \( \frac{125}{v^{6}} \).
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Simplify this solution Bonus Knowledge
To simplify \( \left(5 v^{-2}\right)^{3} \), start by applying the power of a product property, which states that \( (ab)^n = a^n b^n \). So, we will distribute the exponent to both the 5 and \( v^{-2} \): \[ \left(5 v^{-2}\right)^{3} = 5^{3} \cdot (v^{-2})^{3} = 125 \cdot v^{-6}. \] Don't forget that \( v^{-6} \) denotes \( \frac{1}{v^6} \). So, we can write it as: \[ 125 \cdot v^{-6} = \frac{125}{v^6}. \] This gives you the final simplified result!
