Question

Simplify this expression: `\left(20a^{2}b^{-12}c^{-4}\right)\left(3a^{15}b^{12}c^{6}\right)`.

Answer 1

To simplify the expression \(\left(20a^{2}b^{-12}c^{-4}\right)\left(3a^{15}b^{12}c^{6}\right)\), we can start by multiplying the coefficients and then combine the like terms for the variables \(a\), \(b\), and \(c\).

1. **Multiply the coefficients**:
\[
20 \times 3 = 60
\]

2. **Combine the \(a\) terms**:
\[
a^{2} \cdot a^{15} = a^{2+15} = a^{17}
\]

3. **Combine the \(b\) terms**:
\[
b^{-12} \cdot b^{12} = b^{-12 + 12} = b^{0} = 1
\]

4. **Combine the \(c\) terms**:
\[
c^{-4} \cdot c^{6} = c^{-4 + 6} = c^{2}
\]

Now, we combine all of these results together:
\[
60a^{17} \cdot 1 \cdot c^{2} = 60a^{17}c^{2}
\]

Therefore, the simplified expression is:
\[
\boxed{60a^{17}c^{2}}
\]