Question
Simplify. \( \left(3 x^{4}\right)^{5}\left(2 x y^{2}\right)^{3} \) \( [?] x] y \square \)
Ask by Ryan Pollard. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(1944x^{23}y^{6}\).
Solution
Calculate or simplify the expression \( (3x^4)^5(2xy^2)^3 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(3x^{4}\right)^{5}\left(2xy^{2}\right)^{3}\)
- step1: Rewrite the expression:
\(243x^{20}\times 8x^{3}y^{6}\)
- step2: Multiply the numbers:
\(1944x^{20}\times x^{3}y^{6}\)
- step3: Multiply the terms:
\(1944x^{23}y^{6}\)
The simplified expression is \(1944x^{23}y^{6}\).
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Simplify this solution The Deep Dive
To simplify \( \left(3 x^{4}\right)^{5}\left(2 x y^{2}\right)^{3} \), we can start by applying the power of a product rule. First, simplify \( \left(3 x^{4}\right)^{5} \): \[ (3^{5})(x^{4})^{5} = 243 x^{20} \] Next, simplify \( \left(2 x y^{2}\right)^{3} \): \[ (2^{3})(x^{3})(y^{2})^{3} = 8 x^{3} y^{6} \] Now, combine the two results together: \[ 243 x^{20} \cdot 8 x^{3} y^{6} = (243 \cdot 8)(x^{20} \cdot x^{3})(y^{6}) = 1944 x^{23} y^{6} \] Thus, the simplified expression is: \[ 1944 x^{23} y^{6} \]
