Question

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:

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