Problem 104 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(\frac{1}{a^n}\).

Step 2: Apply the negative exponent property to the given expression

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

Step 3: Simplify the expression

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

Step 4: Write the final answer

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