Questions: Exponents and Exponential Functions Power rules with negative exponents Simplify. (3 b^(-6) c^(4))^(-4) Write your answer using only positive exponents.

Solution Steps

We start with the expression \((3 b^{-6} c^{4})^{-4}\). By applying the power of a power rule, we distribute the exponent \(-4\) to each term inside the parentheses: \[ (3)^{-4} (b^{-6})^{-4} (c^{4})^{-4} \]

Next, we simplify each term:

• \((3)^{-4} = \frac{1}{3^4} = \frac{1}{81}\)
• \((b^{-6})^{-4} = b^{24}\)
• \((c^{4})^{-4} = c^{-16} = \frac{1}{c^{16}}\)

Combining these results, we have: \[ \frac{1}{81} b^{24} \cdot \frac{1}{c^{16}} = \frac{b^{24}}{81 c^{16}} \]

Final Answer