Exponent Rules
x^a = x*x*.... (a times)
Example: 2⁵ = 2*2*2*2*2 = 32

x^(a+b) = (x^a)(x^b)
Example: 2⁽²⁺³⁾ = 2⁵ = 32 = 4*8 = (2²)(2³)

x^(a-b) = (x^a)/(x^b)
Example: 2^(3-2) = (2³)/(2²) = 8/4 = 2 = 2¹ = 2^(3-2)

x^(-b) = 1/(x^b)
Example: 2^(-3) = 1/(2³) = 1/8

x^(a*b) = (x^a)^b = (x^b)^a
Example: 2^(2*3) = 2⁶ = 64 = 4³ = (2²)³ = 8² = (2³)²

if y = x^a then x = y^(1/a)
Example: 8 = 2³ so 2 = 8^(1/3)

x^(1/b) = bth root of x

x^(a/b) = (x^a)^(1/b)
Example: 8^(2/3) = (8²)^(1/3) = 64^(1/3) = 4
Check: 4^(3/2) = (4*4*4)^1/2 = 64^(1/2) = (8*8)^1/2 = 8

Decimal example:
16^(1.25) = 16^{(1 + .25)} = (16¹)(16^(1/4)) = 16*2 = 32
Alternate: 16^(1.25) = (2⁴)^(5/4) = 2^(4*5/4) = 2⁵ = 32
Check: 32^(.8) = 32^(4/5) = (32⁴)^1/5 = 16