Negative and Zero Exponents
A free Pre-Algebra lesson from the “Decimals, Roots, and the Real Number System” unit, with a worked example and practice problems including step-by-step solutions.
Any nonzero number raised to the zero power equals 1. A negative exponent means take the reciprocal: a^(-n) = 1 / a^n. Combined with the product, quotient, and power rules, negative and zero exponents let you write very small numbers compactly. In Decimals, Roots, and the Real Number System, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Use the rule that any nonzero number to the zero power equals 1
- Evaluate negative exponents as reciprocals of positive-exponent forms
- Apply exponent rules with negative or zero exponents
Worked example
Problem. Evaluate 5^(-2).
- A negative exponent means take the reciprocal of the positive-exponent form.
- 5^(-2) = 1 / 5^2.
- 5^2 = 25, so the answer is 1/25.
- Connect the calculation back to Negative and Zero Exponents so the method, not just the arithmetic, is clear.
Answer: 1/25
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response). Counts include repeated prompts and variants.
Practice problems
1. Evaluate 4^0.
Show solution
- Anything (nonzero) raised to the zero power is 1.
- 4^0 = 1.
Answer: 1
2. Evaluate 7^0.
Show solution
- Same rule: anything nonzero to the 0 power is 1.
- 7^0 = 1.
Answer: 1
3. Evaluate 2^(-3).
Show solution
- Negative exponent: reciprocal of 2^3.
- 2^3 = 8, so 2^(-3) = 1/8.
Answer: 1/8
4. Evaluate 10^(-2).
Show solution
- 10^(-2) = 1 / 10^2.
- 10^2 = 100, so the answer is 1/100.
Answer: 1/100
5. Evaluate 3^(-1).
Show solution
- A negative-one exponent is just the reciprocal.
- 3^(-1) = 1/3.
Answer: 1/3
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