Mathematical exponent Integral rule

Integral rule

∫ X ⁿ dx = X ⁿ⁺¹/ (n+1) + C

For example,

∫ X³dx = X³⁺¹/ (3+1) + C = X⁴/4+C

Mathematical exponent Derivative rule

Derivative rule

(Aⁿ)’ = n x A^n-1

For example,

(A⁴)’ = 4 x A^4-1 = 4 x A³

Mathematical exponent minus one rule

Minus one rule

(-1) ⁿ = 1 if n is even, -1 if n is odd

For example,

(-1)⁹ = -1

(-1)⁶ = 1

Mathematical exponent Negative exponents rule

Negative exponents rule

B ^-n = 1 / B ⁿ

For example,

2^-4 = 1/2⁴ = 1 / (2x2x2x2) = 1/16 = 0.0625

Mathematical exponent Power rule

Power rule I

(Aⁿ) ^m = A ^{(n x m)}

For example,

(2³)² = 2^3x2 = 2⁶ = 2x2x2x2x2x2 = 64

Power rule II

A^{n ^ m} = A ^{(n ^ m)}

For example,

2^{3^2} = 2^{(3^2)} = 2^(3x3) = 2⁹ = 2x2x2x2x2x2x2x2x2 = 512

Power rule with radicals

^m√ (Aⁿ) = A ^n/m

For example,

²√ (2⁶) = 2^6/2 = 2³ = 2x2x2 = 8

Mathematical exponent Quotient rule

Quotient rule with same base

Aⁿ / A^m = A^n-m

For example,

2⁴ / 2² = 2^4-2 = 2² = 2x2 = 4

           

Quotient rule with same exponent

Aⁿ / Zⁿ = (A / Z) ⁿ

For example,

9² / 3² = (9/3)² = 3² = 3x3 = 9