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

1 answer

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: \[ \frac{1}{6^{9}} \]