What are Exponents?
Exponents show how many times a number, called the base, is multiplied by itself. They're a compact way to write repeated multiplication and are essential for scientific notation, growth models, and algebra.
An exponent n tells you how many times to multiply the base a by itself: aⁿ = a × a × ... × a (n times). For example, 2³ = 2 × 2 × 2 = 8.
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Step-by-step worked examples
Calculate 2⁵.
2⁵ means 2 multiplied by itself 5 times 2×2×2×2×2 = 32
Simplify 3² × 3⁴ using the product rule.
Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ 3² × 3⁴ = 3^(2+4) = 3⁶ = 729
Evaluate 5⁰.
Zero exponent rule: any nonzero base to the power 0 equals 1 5⁰ = 1
Flashcards
Quick quiz
Q1.What is 4³?
Q2.Simplify x⁵ × x³.
Q3.What is 7⁰?
Q4.What is 2⁻³?
The full card deck, worked steps and AI-tutor support for “What are Exponents?” are in Notek — study by hand before your exam.
Common mistakes
Thinking aⁿ means a × n instead of repeated multiplication. — Correct: aⁿ means a multiplied by itself n times, e.g. 2³ = 2×2×2 = 8, not 2×3 = 6.
Adding exponents when multiplying different bases, like 2³ × 3² = 6⁵. — Correct: The product rule only applies to the SAME base: aᵐ × aⁿ = aᵐ⁺ⁿ.
Thinking a negative exponent makes the result negative. — Correct: A negative exponent means 'take the reciprocal', not 'make negative': a⁻ⁿ = 1/aⁿ.
Forgetting that a⁰ = 1 for any nonzero a. — Correct: Any nonzero base raised to the power 0 always equals 1, regardless of the base's value.
FAQ
What is the formula for exponents?
aⁿ = a × a × ... × a (n times), where a is the base and n is the exponent.
What are exponents in simple terms?
A shorthand for repeated multiplication of the same number, e.g. 2⁴ means 2 multiplied by itself 4 times.
How to calculate exponents step by step?
Multiply the base by itself as many times as the exponent indicates, or use rules like the product and power rules for expressions.
What are examples of exponents?
2³ = 8, 10² = 100, and 5⁻¹ = 1/5 are all common exponent examples.