Question
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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: \[ \frac{16 z^{8}}{25} \]

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