Question
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Tutor-Verified Answer
Answer
\( \frac{1}{z^{10}} \)
Solution
Calculate or simplify the expression \( (z^{-5})^{2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(z^{-5}\right)^{2}\)
- step1: Multiply the exponents:
\(z^{-5\times 2}\)
- step2: Multiply the numbers:
\(z^{-10}\)
- step3: Simplify:
\(\frac{1}{z^{10}}\)
The simplified form of \( \left(z^{-5}\right)^{2} \) is \( \frac{1}{z^{10}} \).
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Simplify this solution Mind Expander
To simplify \( \left(z^{-5}\right)^{2} \), you can use the power of a power rule in exponents, which states that \( (a^m)^n = a^{m \cdot n} \). So, applying this to your expression gives you \( z^{-5 \cdot 2} = z^{-10} \). Voilà! Now when you encounter negative exponents, don't forget that you can also express them as fractions: \( z^{-10} = \frac{1}{z^{10}} \). So, if you prefer your answer in a fraction form, there you have it!
