Question
5. \( 5\left(3 a^{-2} b\right)^{3}\left(2 a b^{3}\right) \)
Ask by Marshall Bartlett. in the Philippines
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of the expression is \(\frac{270b^{6}}{a^{5}}\).
Solution
Calculate or simplify the expression \( 5*(3*a^(-2)*b)^3*(2*a*b^3) \).
Simplify the expression by following steps:
- step0: Solution:
\(5\left(3a^{-2}b\right)^{3}\left(2ab^{3}\right)\)
- step1: Evaluate:
\(5\left(3a^{-2}b\right)^{3}\times 2ab^{3}\)
- step2: Multiply the terms:
\(10\left(3a^{-2}b\right)^{3}ab^{3}\)
- step3: Multiply the terms:
\(270a^{-6}b^{3}ab^{3}\)
- step4: Multiply the terms:
\(270a^{-5}b^{3}\times b^{3}\)
- step5: Multiply the terms:
\(270a^{-5}b^{6}\)
- step6: Simplify:
\(\frac{270b^{6}}{a^{5}}\)
The simplified form of the expression \(5\left(3 a^{-2} b\right)^{3}\left(2 a b^{3}\right)\) is \(\frac{270b^{6}}{a^{5}}\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \( 5\left(3 a^{-2} b\right)^{3}\left(2 a b^{3}\right) \), we'll start by working through the components step by step. First, simplify \( \left(3 a^{-2} b\right)^{3} \): \[ (3^3)(a^{-2})^3(b^3) = 27 a^{-6} b^3 \] Now, multiply this by \( 2 a b^3 \): \[ 27 a^{-6} b^3 \cdot 2 a b^{3} = 54 a^{-6 + 1} b^{3 + 3} = 54 a^{-5} b^6 \] Finally, multiply by the 5 from the original expression: \[ 5 \cdot 54 a^{-5} b^6 = 270 a^{-5} b^6 \] So the simplified expression is: \[ \boxed{270 a^{-5} b^6} \]
