Review

Property	Rule	Examples
Multiplication Properties
	x^mxⁿ = x^(m+n) When multiplying like bases, add the exponents	c²c⁵c⁶ = c²⁺⁵⁺⁶ = c¹³ (a³b⁴)(a²b⁵) = a³⁺² b⁴⁺⁵ = a⁵b⁹
	(x^m)ⁿ = x^{(m • n)} When raising a power to another power, multiply the exponents.	(y⁴)⁵ = y^4•5 = y²⁰
	(xy)ⁿ= xⁿyⁿ To raise a product (multiplication) inside parentheses to a power, apply that power to each factor inside the parentheses.	(p³q²)⁴ = p^3•4q^2•4 = p¹²q⁸
	x⁰ = 1 Anything to the zero power is equal to 1.	(2x⁵y⁶z⁸)⁰ = 1

Property	Rule	Example
Division Properties
	= a^{m – n} When dividing like bases, subtract the exponents. Simplify coefficients (the numbers in front of the variables) as usual.	= x^{7 – 3} = x⁴
	= When raising a fraction to a power, apply the power to both the numerator and denominator.	=
	a^–n = If the exponent is negative, flip the base and exponent to the other side of the fraction line and make the exponent positive.	x^–3 = = y⁵