Questions: Choose the expression that is equivalent to (6^(-3) / (3^(-2) * 6^2))^3. 3^6 / 6^15 3^2 / 6^5 -3^6 / 6^15 -3^2 / 6^5

Solution Steps

Start by simplifying the expression inside the parentheses: \[ \left(\frac{6^{-3}}{3^{-2} \cdot 6^{2}}\right) \] Rewrite the expression using the properties of exponents: \[ \frac{6^{-3}}{3^{-2} \cdot 6^{2}} = 6^{-3} \cdot 3^{2} \cdot 6^{-2} \]

Combine the terms with the same base: \[ 6^{-3} \cdot 6^{-2} = 6^{-5} \] So the expression becomes: \[ 6^{-5} \cdot 3^{2} \]

Now, raise the entire expression to the power of 3: \[ \left(6^{-5} \cdot 3^{2}\right)^{3} = 6^{-15} \cdot 3^{6} \] Rewrite the expression as a fraction: \[ \frac{3^{6}}{6^{15}} \]

Final Answer