Question
Multiply. \[ \left(-10 y^{2} z^{4}\right)\left(-3 y^{3} z^{3}\right) \]
Ask by Rojas Munoz. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Multiply the coefficients and add the exponents for like bases:
\[
30\, y^{5}\, z^{7}
\]
Solution
To multiply the expressions \((-10 y^{2} z^{4})\) and \((-3 y^{3} z^{3})\), follow these steps:
1. **Multiply the Coefficients:**
\[
(-10) \times (-3) = 30
\]
2. **Multiply the Like Bases by Adding Exponents:**
- For \(y\):
\[
y^{2} \times y^{3} = y^{2+3} = y^{5}
\]
- For \(z\):
\[
z^{4} \times z^{3} = z^{4+3} = z^{7}
\]
3. **Combine the Results:**
\[
30 y^{5} z^{7}
\]
**Final Answer:**
\[
30\, y^{5}\, z^{7}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
When you multiply the two expressions, you simply multiply the coefficients and then combine like terms. First, multiply the coefficients: \(-10 \times -3 = 30\). Next, for the variables, you add the exponents of like bases: For \(y\), \(y^2 \times y^3 = y^{2+3} = y^5\). For \(z\), \(z^4 \times z^3 = z^{4+3} = z^7\). Putting it all together, we get: \[ 30 y^5 z^7 \] So, the final answer is: \[ 30 y^5 z^7 \]
