4a³b*(3ab) as indices

Answer 1

To simplify the expression \(4a^3b \cdot (3ab)\) using indices, follow these steps:

1. Multiply the coefficients: Multiply the numerical coefficients together. \(4 \cdot 3 = 12\).

2. Combine the variables using the laws of indices:

   • For \(a\): \[ a^3 \cdot a^1 = a^{3+1} = a^4 \]
   • For \(b\): \[ b^1 \cdot b^1 = b^{1+1} = b^2 \]

Putting it all together, we have:

\[ 4a^3b \cdot (3ab) = 12a^4b^2 \]

So, the simplified expression is:

\[ \boxed{12a^4b^2} \]