Problem 64 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(\frac{4 a^{-5} b^{3}}{12 a^{3} b^{-5}}\right)^{0}$$

Step-by-Step Solution

Answer

The simplified form of the given exponential expression is \( 1 \).

Step 1: Identify the expression

The given expression is \( \left(\frac{4 a^{-5} b^{3}}{12 a^{3} b^{-5}}\right)^{0} \).

Step 2: Apply the rule of exponentiation

When any expression is raised to the power zero, irrespective of what the expression is, the result is always 1.

Step 3: Result

Therefore, \( \left(\frac{4 a^{-5} b^{3}}{12 a^{3} b^{-5}}\right)^{0} = 1 \). This can be cross-checked by evaluating the expression inside the bracket, which will lead to the same result.