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 one rules

One rules I

b¹ = b

For example,

9¹ = 1

One rules II

1ⁿ = 1

For example,

1⁶ = 1

Mathematical exponent Zero rules

Zero rules I

b⁰ = 1

For example,

9⁰ = 1

Zero rules II

0ⁿ = 0, for n>0

For example,

0⁶ = 0

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