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Answer
The simplified form is \( \frac{1}{4m^{8}} \).
Solution
Calculate or simplify the expression \( (2m^4)^{-2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2m^{4}\right)^{-2}\)
- step1: Use the properties of exponents:
\(2^{-2}\left(m^{4}\right)^{-2}\)
- step2: Evaluate the power:
\(\frac{1}{4}m^{-8}\)
- step3: Simplify:
\(\frac{1}{4m^{8}}\)
The simplified form of \( \left(2 m^{4}\right)^{-2} \) is \( \frac{1}{4m^{8}} \).
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Simplify this solution The Deep Dive
To simplify \( \left(2 m^{4}\right)^{-2} \), we first apply the negative exponent rule, which means we take the reciprocal of the base raised to the positive exponent. This gives us: \[ \frac{1}{(2 m^{4})^{2}} \] Next, we square both the coefficient and the variable separately: \[ \frac{1}{2^{2} (m^{4})^{2}} = \frac{1}{4 m^{8}} \] So, the final simplified expression is: \[ \frac{1}{4 m^{8}} \]
