Problem 63 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(\frac{3 a^{-5} b^{2}}{12 a^{3} b^{-4}}\right)^{0}$$

Step-by-Step Solution

Answer

The simplified form of the given expression \(\left(\frac{3 a^{-5} b^{2}}{12 a^{3} b^{-4}}\right)^{0}\) is 1.

Step 1: Apply the exponent rule to the whole expression

Apply the universal rule that any number or expression to the power of 0 equals 1. So, \(\left(\frac{3 a^{-5} b^{2}}{12 a^{3} b^{-4}}\right)^{0}= 1\)

Step 2: Clarify why the rule is applied

This is because any nonzero number to the power 0 equals 1, irrespective of the complexity of the number/expression.