Question
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Answer
\( 125^{-\frac{4}{3}} = \frac{1}{625} \)
Solution
Calculate or simplify the expression \( 125^{-\frac{4}{3}} \).
Calculate the value by following steps:
- step0: Calculate:
\(125^{-\frac{4}{3}}\)
- step1: Express with a positive exponent:
\(\frac{1}{125^{\frac{4}{3}}}\)
- step2: Evaluate the power:
\(\frac{1}{625}\)
The value of \(125^{-\frac{4}{3}}\) is \(\frac{1}{625}\) or approximately 0.0016.
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Simplify this solution The Deep Dive
To solve \( 125^{-\frac{4}{3}} \), we can start by rewriting it in a more manageable form. We know that \( 125 = 5^3 \), so we can express this as \( (5^3)^{-\frac{4}{3}} \). Using the power of a power property \( (a^m)^n = a^{m \cdot n} \), we have: \[ (5^3)^{-\frac{4}{3}} = 5^{3 \cdot -\frac{4}{3}} = 5^{-4} \] Now, \( 5^{-4} \) can be rewritten as \( \frac{1}{5^4} \). Calculating \( 5^4 \): \[ 5^4 = 625 \] So, \[ 125^{-\frac{4}{3}} = \frac{1}{625} \] And there you have the final answer!
