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Chapter 0: Problem 64

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

Short Answer

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

Step by step solution

01

Identify the expression

The given expression is \( \left(\frac{4 a^{-5} b^{3}}{12 a^{3} b^{-5}}\right)^{0} \).
02

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.
03

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.

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