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Properties of Exponents

Let a and b be real numbers, variables, or algebraic expressions, and let m and n be integers. (All denominators and bases are nonzero.)
a data set by xnity
created February 27, 2016
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PropertyExample
a^m * a^n = a^(m + n)3^2 * 3^4 = 3^(2 + 4) = 3^6 = 729
(a^m)/(a^n) = a^(m - n)(x^7)/(x^4) = x^(7 - 4) = x^3
a^-n = 1/a^n = (1/a)^ny^-4 = 1/y^4 = (1/y)^4
a^0 = 1, a /= 0(x^2 + 1)^0 = 1
(ab)^m = a^m * b^m(5x)^3 = 5^3 * x^3 = 125x^3
(a^m)^n = a^(mn)(y^3)^-4 = y^(3*-4) = y^-12 = 1/y^12
(a/b)^m = a^m/b^m(2/x)^3 = (2^3)/(x^3) = 8/(x^3)
|a^2| = |a|^2 = a^2|(-2)^2| = |-2|^2 = 2^2 = 4
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