Question

which number equals \\(5^{-2}\\)?

• \\(-25\\)
• \\(-\frac{1}{10}\\)
• \\(\frac{1}{10}\\)
• \\(\frac{1}{25}\\)

Explanation:

Apply negative exponent rule

Using the Evaluating Exponential Expressions knowledge point

$$ a^{-n} = \frac{1}{a^n} $$

Substitute the given values

Using the Evaluating Exponential Expressions knowledge point

$$ 5^{-2} = \frac{1}{5^2} $$

Evaluate the denominator

Using the Evaluating Exponential Expressions knowledge point

$$ 5^2 = 5 \times 5 = 25 $$

Write the final fraction

Using the Evaluating Exponential Expressions knowledge point

$$ 5^{-2} = \frac{1}{25} $$

Answer:

• -25
• -\(\frac{1}{10}\)
• \(\frac{1}{10}\)
• \(\frac{1}{25}\) (Correct answer)