Question
Simplify. Express your answer using positive exponents. \( \left(5 z^{7}\right)\left(8 z^{-1}\right)\left(6 z^{3}\right) \) \begin{tabular}{l} Submit \\ \( \square \square \square \) \\ \hline\end{tabular}
Ask by Washington Adkins. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 240z^9 \)
Solution
1. Multiply the numerical coefficients:
\( 5 \times 8 \times 6 = 240 \).
2. Multiply the variables by adding their exponents (using the rule \( z^a \times z^b = z^{a+b} \)):
\( z^7 \times z^{-1} \times z^3 = z^{7 + (-1) + 3} = z^9 \).
3. Combine the results:
\( 240 \times z^9 = 240z^9 \).
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Simplify this solution Beyond the Answer
To simplify \( \left(5 z^{7}\right)\left(8 z^{-1}\right)\left(6 z^{3}\right) \), we start by multiplying the coefficients together: \(5 \times 8 \times 6 = 240\). Next, we combine the \(z\) terms by adding the exponents: \[ z^{7} \times z^{-1} \times z^{3} = z^{7 + (-1) + 3} = z^{9}. \] Putting it all together, we have \[ 240 z^{9}. \] So, the simplified expression is: \(\boxed{240 z^{9}}\)
