Work out exponent rules instantly with clear inputs, formula shown and shareable results.
The index laws all follow from counting factors: multiplying powers of the same base adds the exponents, dividing subtracts them, and raising a power to a power multiplies them.
Product rule
bᵐ × bⁿ = bᵐ⁺ⁿ
Quotient rule
bᵐ ÷ bⁿ = bᵐ⁻ⁿ
Power rule
(bᵐ)ⁿ = bᵐⁿ
2⁸ = 256, 2² = 4 and 2¹⁵ = 32768.
Because bᵐ ÷ bᵐ = bᵐ⁻ᵐ = b⁰, and any non-zero number divided by itself is 1.