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LAWS OF EXPONENTS Monomial is an expression that is a number, a variable, or a product of a number and variables. Power is the expression of the form xn. Laws of Exponents Multiplying Powers: a a a m n Power of a Power a a m n mn mn Laws of Exponents m Dividing Powers: Power of a Product: a n a a mn ab a b m m m Laws of Exponents Power of Zero: a 0 1 Examples using the laws of exponents: 1. x² ·x³= x²+³ 2. (x²)³= x²•³ Keep the base Add the exponents Keep the base Multiply the exponents Examples using the laws of exponents: 12 Keep the base x 8 Subtract the exponents 3. 4 x x Raise each base to the 4. (xy)³= x³y³ exponent Then multiply By definition 25 is the number you would multiply times itself to get 25 for an answer. Because we are familiar with multiplication, we know that 25 = 5 Numbers like 25, which have whole numbers for their square roots, are called perfect squares You need to memorize at least the first 15 perfect squares SQUARE ROOTS Perfect square 1 Square root Square root 1 = 1 Perfect square 81 81 = 9 4 4 = 2 100 100 = 10 9 9 = 3 121 121 = 11 16 16 = 4 144 144 = 12 25 25 = 5 169 169 = 13 36 36 = 6 196 196 = 14 49 49 = 7 225 225 = 15 64 64 = 8