4a^3 b ×(3ab)^-3

Answer 1

To simplify the expression \( 4a^3 b \times (3ab)^{-3} \), we'll start by simplifying the second part of the expression, \((3ab)^{-3}\).

1. Rewrite \((3ab)^{-3}\): \[ (3ab)^{-3} = \frac{1}{(3ab)^3} = \frac{1}{3^3 \cdot a^3 \cdot b^3} = \frac{1}{27 a^3 b^3} \]

2. Now substitute this back into the original expression: \[ 4a^3 b \times (3ab)^{-3} = 4a^3 b \times \frac{1}{27 a^3 b^3} \]

3. Multiply the terms together: \[ = \frac{4a^3 b}{27 a^3 b^3} \]

4. Now, simplify the fraction:

   • The \(a^3\) in the numerator and denominator cancel out: \[ = \frac{4}{27 b^2} \quad \text{(since } b \text{ in the numerator cancels with one } b \text{ in the denominator, leaving } b^2 \text{ in the denominator)} \]

Thus, the simplified expression is:

\[ \frac{4}{27b^2} \]