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Chapter 3: Problem 104

For the following problems, evaluate each numerical expression. $$ 7^{-1} $$

Short Answer

Expert verified
Answer: \(\frac{1}{7}\)

Step by step solution

01

Recall the properties of negative exponents

When an exponent is negative, it represents the reciprocal of the base raised to the positive exponent. In other words, given an expression \(a^{-n}\), this is equivalent to \(\frac{1}{a^n}\).
02

Apply the negative exponent property to the given expression

Using the property from Step 1, we can rewrite \(7^{-1}\) as \(\frac{1}{7^1}\).
03

Simplify the expression

Now we just need to simplify the expression: \(\frac{1}{7^1} = \frac{1}{7}\).
04

Write the final answer

The evaluated numerical expression is \(\frac{1}{7}\).

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