Problem 11
Question
Evaluate each exponential expression. $$4^{-3}$$
Step-by-Step Solution
Verified Answer
The result of evaluating the expression \(4^{-3}\) is \(1/64\).
1Step 1: Understand the exponent rule
Review the rule for negative exponents. A number with a negative exponent should be inverted (i.e., create a fraction with 1 as the numerator and the base of the power as the denominator) to make the exponent positive.
2Step 2: Apply the negative exponent rule
Apply the exponent rule to \(4^{-3}\). The base is 4 and the exponent is -3. Thus, we need to rewrite this expression as \(1/{4^{3}}\)
3Step 3: Simplify the expression
Now we have \(1/{4^{3}}\), which simplifies to 1/64.
Other exercises in this chapter
Problem 10
Evaluate each expression in Exercises \(1-12,\) or indicate that the root is not a real number. $$\sqrt{144}+\sqrt{25}$$
View solution Problem 11
Evaluate each algebraic expression for the given value or values of the variable(s). $$x^{2}-3(x-y), \text { for } x=8 \text { and } y=2$$
View solution Problem 11
Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. $$\frac{y^{2}+7 y-18}{y^{2}-3 y
View solution Problem 11
$$\text { Factor by grouping.}$$ $$x^{3}-2 x^{2}+5 x-10$$
View solution