Exponents — Rules You Must Know Cold

Product rule: x^a times x^b = x^(a+b)

Quotient rule: x^a / x^b = x^(a-b)

Power rule: (x^a)^b = x^(ab)

Zero exponent: x^0 = 1

Negative exponent: x^(-a) = 1/x^a

Radicals:

sqrt(x) = x^(1/2)

Cube root of x = x^(1/3)

Simplifying radicals:

sqrt(50) = sqrt(25 times 2) = 5 sqrt(2)

sqrt(72) = sqrt(36 times 2) = 6 sqrt(2)

SAT pattern: "If 2^x = 32, what is x?" Answer: 2^5 = 32, so x = 5.

Powers to memorize: 2^10 = 1024. 3^4 = 81. 5^3 = 125. 4^3 = 64.

Reference:

Wikipedia: Exponentiation

https://en.wikipedia.org/wiki/Exponentiation