The basic idea: repeated multiplication
2^5 means 2 multiplied by itself 5 times: 2 × 2 × 2 × 2 × 2 = 32. Similarly, 3^4 means 3 × 3 × 3 × 3 = 81.
What a negative exponent means
A negative exponent doesn't mean a negative result — it means the reciprocal of the positive-exponent version. 5^-2 is 1 ÷ 5² = 1 ÷ 25 = 0.04, not a negative number at all.
Why negative exponents work this way
Exponents follow a pattern where each step down by 1 divides the previous result by the base: 5² = 25, 5¹ = 5, 5⁰ = 1, and continuing that same pattern below zero, 5⁻¹ = 1 ÷ 5 = 0.2, and 5⁻² = 0.2 ÷ 5 = 0.04 — consistent with the direct reciprocal calculation.
What exponentiation doesn't answer
Exponentiation answers "base raised to this power gives what result?" Two closely related but different questions — "what power gives this result?" and "what base gives this result?" — are answered by logarithms and roots instead, covered in the companion articles.