4a^3b*(3ab)^-2

Answer 1

To simplify the expression \( 4a^3b(3ab)^{-2} \), we will start with the component inside the parentheses:

1. Simplify \((3ab)^{-2}\): \[ (3ab)^{-2} = \frac{1}{(3ab)^2} = \frac{1}{9a^2b^2} \]

2. Now, substitute back into the original expression: \[ 4a^3b(3ab)^{-2} = 4a^3b \cdot \frac{1}{9a^2b^2} \]

3. Multiply the terms together: \[ = \frac{4a^3b}{9a^2b^2} \]

4. Simplify the fraction by canceling out like terms:

   • The \( b \) in the numerator and \( b^2 \) in the denominator simplifies to \( \frac{1}{b} \).
   • The \( a^3 \) in the numerator and \( a^2 \) in the denominator simplifies to \( a^{3-2} = a^1 = a \).

   So, we have: \[ = \frac{4a}{9b} \]

Thus, the simplified expression is: \[ \frac{4a}{9b} \]