Question

Which is the simplified form of the expression (6 Superscript negative 2 Baseline times 6 Superscript 5 Baseline) Superscript negative 3?
6 Superscript 30
StartFraction 1 Over 6 Superscript 9 EndFraction
6 Superscript 0
StartFraction 1 Over 6 Superscript 13 Baseline EndFraction

Answer 1

To simplify the expression \((6^{-2} \times 6^5)^{-3}\), we can follow these steps:

1. **Combine the exponents** within the parentheses:
\[
6^{-2} \times 6^5 = 6^{-2 + 5} = 6^{3}
\]

2. **Raise the result to the power of -3**:
\[
(6^{3})^{-3} = 6^{3 \times -3} = 6^{-9}
\]

3. **Express \(6^{-9}\)** in a simplified form:
\[
6^{-9} = \frac{1}{6^9}
\]

Thus, the simplified form of the original expression is:
\[
\frac{1}{6^9}
\]

Therefore, the answer is:
\[
\frac{1}{6^{9}}
\]