Exponent Rules  dward
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Quick List of Exponent Rules
 Zero
 Negative
 Product of Powers
 Power to Power
 Power of Product
 Quotient of Powers
 Power of Quotient
 Fractional

x^{0} = 1
Zero Exponent Rule

Zero Exponent Rule
x^{0}^{ }= 1; Any value raised to the zero power equals 1.

Negative Exponent Rule
x^{y} = 1/x^{y} To remove a negative from an exponent move the term down to the denominator or up to the numerator.

x^{y} = 1/x^{y}
Negative Exponent Rule

1/x^{y} = x^{y}
Negative Exponent Rule

Product of Powers
 x^{m} * x^{n} = x^{m+n }When multiplying powers with the same base simplify by keeping the base and adding the powers.^{}

x^{m} * x^{n} = x^{m+n}
Product of Powers

Power to a Power
 (x^{m})^{n} = x^{m*n } When a power is the base of another power to simplify multiply the exponents.^{}

(x^{m})^{n} = x^{m*n}
Power to a Power

Power of a Product
(ab)^{m} = a^{m} * b^{m }When a product is raised to a power "distribute" the exponent to every factor.

(ab)^{m} = a^{m} * b^{m}
Power of a Product

Quotient of Powers
x^{m} / x^{n} = x^{mn }When dividing powers with the same base simplify by keeping the base and subtracting the exponent of the divisor from the exponent of the dividend (Dividend / Divisor = Quotient)

x^{m} / x^{n} = x^{mn}
Quotient of Powers

Power of a Quotient
 (a/b)^{m} = a^{m} / b^{m }When a quotient is raised to a power "distribute" the exponent to the dividend and the divisor.^{}

(a/b)^{m} = a^{m} / b^{m}
Power of a Quotient

Fractional Power
x^{m/n} = the n^{th} root of x all raised to the m^{th} power OR the n^{th} root of x^{m} "n" is the index and "m" is the exponent.

x^{m/n} = the n^{th} root of x all raised to the m^{th} power OR the n^{th} root of x^{m} "n" is the index and "m" is the exponent.
Fractional Power

List of Exponent Rules with brief clue what to do
 Zero : One
 Negative : Move down or up
 Product of Powers : Add
 Power to Power : Multiply
 Power of Product : Distribute
 Quotient of Powers : Subtract
 Power of Quotient : Distribute
 Fractional : Denominator is Index, Numerator is Exponent