Question
1. \( \left(2 x^{-5} y^{8} z^{2}\right)\left(3 x^{2} y^{-3} z\right) \)
Ask by Higgins Joseph. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{6 y^{5} z^{3}}{x^{3}}
\]
Solution
To simplify the expression \( \left(2 x^{-5} y^{8} z^{2}\right)\left(3 x^{2} y^{-3} z\right) \), follow these steps:
1. **Multiply the coefficients:**
\[
2 \times 3 = 6
\]
2. **Multiply the \(x\) terms:**
\[
x^{-5} \times x^{2} = x^{-3}
\]
3. **Multiply the \(y\) terms:**
\[
y^{8} \times y^{-3} = y^{5}
\]
4. **Multiply the \(z\) terms:**
\[
z^{2} \times z = z^{3}
\]
Putting it all together:
\[
6 \times x^{-3} \times y^{5} \times z^{3}
\]
To express the result with positive exponents, rewrite \(x^{-3}\) as \(\frac{1}{x^{3}}\):
\[
\frac{6 y^{5} z^{3}}{x^{3}}
\]
**Final Simplified Expression:**
\[
\boxed{\dfrac{6\, y^{5} z^{3}}{\,x^{3}\,}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
First, let's combine the coefficients and each of the variable parts separately. The coefficients multiply to \(2 \times 3 = 6\). For the variables, we add exponents when multiplying: - For \(x\), we have \(-5 + 2 = -3\) so it becomes \(x^{-3}\). - For \(y\), \(8 - 3 = 5\) so it becomes \(y^{5}\). - For \(z\), \(2 + 1 = 3\) so it becomes \(z^{3}\). Putting it all together, we get: \[ 6 x^{-3} y^{5} z^{3} \] To express this in a more traditional format, you could rewrite it as: \[ \frac{6 y^{5} z^{3}}{x^3} \]
