PROPERTIES OF EXPONENTS SQUARE ROOTS 8THº Math TEACHER ANDREA BARRIA POWERS OF EXPONENTS The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In 82 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64 • In words: 82 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared" 1. Example: 24 = 2 × 2 × 2 × 2 = 16 the power is 4: "2 to the power 4 is 16" or we can say the power is the result of 16: "the 4th power of 2 is 16 2. Example: 53 = 5 × 5 × 5 = 125 In words: 53 could be called "5 to the third power", "5 to t or simply "5 cubed" he power 3" MULTIPLICATION • 1. Product of Powers Examples 1. Since the Powers have the same base, keep the base and add the exponents. 2. Group powerswith the same base together. 3. Add the exponents of power with the same base. 1. Group Powers with the same base together. 2. Add the exponentsof Powers with the same base. 3. Group the positive exponents and add sincethey have the same base 4. Add the like bases. MULTIPLICATION • 2. power of a product • Each base raise to the same exponent Examples MULTIPLICATION • 3. Power of a power property 1. Use the power of a power property 2. Multiply the exponents Zero multiplied by any number is zero. Any number raised to the zero is 1 Examples 1. Use the power of a power property 2. Simplify the exponent of the first term. 3. Use the product of a power property with the same base 4. Write with a positive exponent 1. Use the power of a power property 2. Simplify each term 3. Add the exponents PROBLEM SOLVING PROBLEM SOLVING DIVISION Examples DIVISION Examples Use the power property and simplify Examples Use the power of a product property Use the power of a quotient and simplify Examples NEGATIVE POWER Examples 1. Change or rewrite the expresión with a positive exponent 2. Use the Powers of a quotient property Examples SQUARE ROOT • Roots" (or "radicals") are the "opposite" operation of applying exponents; we can "undo" a power with a radical, and we can "undo" a radical with a power. For instance, if we square 2, we get 4, and if we "take the square root of 4", we get 2; if we square 3, we get 9, and if we "take the square root of 9", we get 3. Any number raised to the power of 2 can be modeled using a polygon--the square! That's why we call raising a number to the second power "squaring the number." The perfect squares are squares of whole numbers. Here are the first five perfect squares. Examples Examples Find out how the answer was obtained