Question
Simplify the expression. Write the answer with positive exponents only. Assume all variables represent nonzero real numbers. \[ \left(-5 y_{0}^{-7} z\right)\left(7 y^{6} z^{6}\right)=\square \]
Ask by Barker May. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \(-\frac{35z^{7}}{y}\).
Solution
Calculate or simplify the expression \( (-5*y^{-7}*z)*(7*y^6*z^6) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-5y^{-7}z\right)\left(7y^{6}z^{6}\right)\)
- step1: Evaluate:
\(\left(-5y^{-7}z\right)\times 7y^{6}z^{6}\)
- step2: Remove the parentheses:
\(-5y^{-7}z\times 7y^{6}z^{6}\)
- step3: Multiply the terms:
\(-35y^{-7}zy^{6}z^{6}\)
- step4: Multiply the terms:
\(-35y^{-7+6}z\times z^{6}\)
- step5: Add the numbers:
\(-35y^{-1}z\times z^{6}\)
- step6: Multiply the terms:
\(-35y^{-1}z^{1+6}\)
- step7: Add the numbers:
\(-35y^{-1}z^{7}\)
- step8: Simplify:
\(-\frac{35z^{7}}{y}\)
The simplified expression is \(-\frac{35z^{7}}{y}\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \((-5 y_{0}^{-7} z)(7 y^{6} z^{6})\), start by multiplying the coefficients and like terms. The coefficients multiply to: \[ -5 \cdot 7 = -35. \] Next, for the \(y\) terms: \[ y_{0}^{-7} y^{6} = y^{-7 + 6} = y^{-1} = \frac{1}{y}. \] Now, for the \(z\) terms: \[ z \cdot z^{6} = z^{1 + 6} = z^{7}. \] Putting it all together: \[ (-35) \cdot \frac{1}{y} \cdot z^{7} = -35 \frac{z^{7}}{y} = -\frac{35 z^{7}}{y}. \] To express the answer with positive exponents only, write the final result as: \[ -\frac{35 z^{7}}{y}. \]
