Question
2. \( \left(2 a b^{-2}\right)\left(a^{-2} b\right) \)
Ask by Mcguire Coles. in the Philippines
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{2}{ab} \).
Solution
Calculate or simplify the expression \( (2ab^{-2})(a^{-2}b) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2ab^{-2}\right)\left(a^{-2}b\right)\)
- step1: Remove the parentheses:
\(2ab^{-2}a^{-2}b\)
- step2: Multiply the terms:
\(2a^{1-2}b^{-2}\times b\)
- step3: Subtract the numbers:
\(2a^{-1}b^{-2}\times b\)
- step4: Multiply the terms:
\(2a^{-1}b^{-2+1}\)
- step5: Add the numbers:
\(2a^{-1}b^{-1}\)
- step6: Simplify:
\(\frac{2}{ab}\)
The simplified form of the expression \( \left(2 a b^{-2}\right)\left(a^{-2} b\right) \) is \( \frac{2}{ab} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To simplify the expression \( \left(2 a b^{-2}\right)\left(a^{-2} b\right) \), you can start by multiplying the coefficients and the variables separately. First, multiply the numerical coefficient: \( 2 \). Next, for the variables, combine the same bases using the property of exponents, which states that \( a^m \cdot a^n = a^{m+n} \). So, for \( a \)'s: \( a^{1} \cdot a^{-2} = a^{1-2} = a^{-1} \). And for \( b \)'s: \( b^{-2} \cdot b^{1} = b^{-2+1} = b^{-1} \). Putting it all together, you get: \[ 2 a^{-1} b^{-1} = \frac{2}{a b} \] Thus, the simplified form is \( \frac{2}{a b} \).
