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Chapter 0: Problem 11

Evaluate each exponential expression. $$ 4^{-3} $$

Short Answer

Expert verified
The evaluated expression \(4^{-3}\) is \(1 / 64\).

Step by step solution

01

Understanding Negative Exponents

In mathematics, a negative exponent indicates the reciprocal of the base. Instead of multiplying the base, it divides it. Therefore, \(4^{-3}\) can be rewritten as \(1/4^3\).
02

Calculating the Reciprocal of the Base

Find the reciprocal of the base by finding the value of the base raised to the positive power. So, \(4^3 = 4*4*4 = 64\).
03

Final Calculation

Finalize the calculation already established. The result is \(1 / 64\).

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