Fowler Chandler
07/20/2023 · Middle School
Use the properties of exponents to rewrite the expression. \( \left(3 x^{4} y^{3}\right)\left(-5 x^{3} y\right) \) A. \( 15 x^{7} y^{4} \) B. \( 15 x^{4} y \) C. \( -15 x^{7} y^{4} \) D. \( -15 x^{1} 2 y^{3} \) Reset Selection
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Step-by-step Solution
To rewrite the expression \( \left(3 x^{4} y^{3}\right)\left(-5 x^{3} y\right) \), we can use the properties of exponents and multiplication.
1. First, multiply the coefficients (the numerical parts):
\[
3 \times -5 = -15
\]
2. Next, combine the \( x \) terms using the property \( x^a \cdot x^b = x^{a+b} \):
\[
x^{4} \cdot x^{3} = x^{4+3} = x^{7}
\]
3. Then, combine the \( y \) terms:
\[
y^{3} \cdot y^{1} = y^{3+1} = y^{4}
\]
Putting it all together, we have:
\[
\left(3 x^{4} y^{3}\right)\left(-5 x^{3} y\right) = -15 x^{7} y^{4}
\]
Thus, the rewritten expression is:
\[
\boxed{-15 x^{7} y^{4}}
\]
The correct answer is C. \( -15 x^{7} y^{4} \).
Quick Answer
The correct answer is C. \( -15 x^{7} y^{4} \).
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