Question
Simplify the expression completely, using only one exponent in your answer: \( \left(\frac{-4 z^{4}}{5}\right)^{2} \)
Ask by Burgess Bartlett. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{16z^{8}}{25} \).
Solution
Calculate or simplify the expression \( ((-4*z^4)/5)^2 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\frac{\left(-4z^{4}\right)}{5}\right)^{2}\)
- step1: Remove the parentheses:
\(\left(\frac{-4z^{4}}{5}\right)^{2}\)
- step2: Rewrite the fraction:
\(\left(-\frac{4z^{4}}{5}\right)^{2}\)
- step3: Rewrite the expression:
\(\frac{\left(4z^{4}\right)^{2}}{5^{2}}\)
- step4: Evaluate the power:
\(\frac{16z^{8}}{25}\)
The simplified expression is \( \frac{16z^{8}}{25} \).
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Bonus Knowledge
To simplify the expression \( \left(\frac{-4 z^{4}}{5}\right)^{2} \), first apply the exponent to both the numerator and the denominator: \[ \frac{(-4)^{2} \cdot (z^{4})^{2}}{5^{2}} = \frac{16 z^{8}}{25} \] Thus, the simplified expression is: \[ \frac{16 z^{8}}{25} \]