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Chapter 0: Problem 11

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

Short Answer

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

Step by step solution

01

Understand the given expression

In the equation \(4^{-3}\), the base is 4 and the exponent is -3. A negative exponent signifies that the base is on the wrong side of the fraction and needs to be reciprocated.
02

Apply the negative exponent rule

The negative exponent rule states that \(a^{-n} = 1/a^n\). Here, a is the base number (in this case 4), and n is the negative power or exponent (in our case -3). So, applying this rule, the expression becomes \(1/{4^3}\).
03

Simplify

Now, \(4^3\) equals 4*4*4 which is 64. Therefore, the final expression transforms to \(1/64\).

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