Question
implify: \( \left(3 x^{4} y\right)^{2} \times x y^{5} \)
Ask by Hampton Ramos. in South Africa
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 9x^{9}y^{7} \)
Solution
To simplify the expression \( \left(3 x^{4} y\right)^{2} \times x y^{5} \), follow these steps:
1. **Expand the squared term:**
\[
\left(3 x^{4} y\right)^{2} = 3^{2} \times \left(x^{4}\right)^{2} \times y^{2} = 9 x^{8} y^{2}
\]
2. **Multiply the expanded term by \( x y^{5} \):**
\[
9 x^{8} y^{2} \times x y^{5} = 9 x^{8+1} y^{2+5} = 9 x^{9} y^{7}
\]
**Final Simplified Expression:**
\[
9x^{9}y^{7}
\]
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Simplify this solution Bonus Knowledge
To simplify the expression \( \left(3 x^{4} y\right)^{2} \times x y^{5} \), start by applying the power of a product rule on the first part: \[ (3 x^{4} y)^{2} = 3^{2} (x^{4})^{2} (y)^{2} = 9 x^{8} y^{2} \] Now, combine this result with the second term in your expression: \[ 9 x^{8} y^{2} \times x y^{5} \] When multiplying like bases, add their exponents: \[ = 9 x^{8+1} y^{2+5} = 9 x^{9} y^{7} \] So, the simplified expression is: \[ \boxed{9 x^{9} y^{7}} \]
