Question
\( 1 \leftarrow \quad \) Use the power rule, the power of a product rule, and the power of a quotient rule to simplify the expression. \[ \left(\frac{-5 x^{2} z^{3}}{y^{4}}\right)^{2} \]
Ask by Henry Munoz. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \frac{25x^{4}z^{6}}{y^{8}} \).
Solution
Calculate or simplify the expression \( ((-5*x^2*z^3)/(y^4))^2 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\frac{\left(-5x^{2}z^{3}\right)}{y^{4}}\right)^{2}\)
- step1: Remove the parentheses:
\(\left(\frac{-5x^{2}z^{3}}{y^{4}}\right)^{2}\)
- step2: Calculate:
\(\left(-\frac{5x^{2}z^{3}}{y^{4}}\right)^{2}\)
- step3: Rewrite the expression:
\(\frac{\left(5x^{2}z^{3}\right)^{2}}{\left(y^{4}\right)^{2}}\)
- step4: Evaluate the power:
\(\frac{25x^{4}z^{6}}{y^{8}}\)
The simplified expression is \( \frac{25x^{4}z^{6}}{y^{8}} \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify the expression \(\left(\frac{-5 x^{2} z^{3}}{y^{4}}\right)^{2}\), we can apply the power of a quotient rule and the power rule. First, we separate the numerator and the denominator: \[ = \frac{(-5)^{2} (x^{2})^{2} (z^{3})^{2}}{(y^{4})^{2}} \] Calculating each part, we get: \[ = \frac{25 x^{4} z^{6}}{y^{8}} \] So the simplified expression is: \[ \frac{25 x^{4} z^{6}}{y^{8}} \]
