Exponent Rules - dward

• Zero
• Negative
• Product of Powers
• Power to Power
• Power of Product
• Quotient of Powers
• Power of Quotient
• Fractional

Zero Exponent Rule

x⁰ = 1; Any value raised to the zero power equals 1.

x^-y = 1/x^y  To remove a negative from an exponent move the term down to the denominator or up to the numerator.

Negative Exponent Rule

Negative Exponent Rule

• x^m * xⁿ = x^m+n   When multiplying powers with the same base simplify by keeping the base and adding the powers.

Product of Powers

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

Power to a Power

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

Power of a Product

x^m / xⁿ = x^m-n   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)

Quotient of Powers

• (a/b)^m = a^m / b^m   When a quotient is raised to a power "distribute" the exponent to the dividend and the divisor.

Power of a Quotient

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

• 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