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Exponents Exponents are a shorthand way to show how many times a number, called the base number, is multiplied times itself. A number with an exponent is said to be "raised to the power" of that exponent. Base Number -- 5 3 -- Exponent The exponent indicates how many times in a row you multiply the base number. Examples: 10 0 = 1 50 = 1 20 = 1 101 =10 51 = 5 21 = 2 102 = 10 ×10 = 100 5 2 = 5 × 5 = 25 22 = 2 × 2 = 4 103 = 10 ×10 ×10 = 1,000 5 3 = 5 × 5 × 5 =125 23 = 2 × 2 × 2 = 8 Laws of Exponents Law Example x1 = x x0 = 1 x-1 = 1/x xmxn = xm+n xm/xn = xm-n (xm)n = xmn (xy)n = xnyn (x/y)n = xn/yn x-n = 1/xn 61 = 6 70 = 1 4-1 = 1/4 x2x3 = x2+3 = x5 x4/x2 = x4-2 = x2 (x2)3 = x2×3 = x6 (xy)3 = x3y3 (x/y)2 = x2 / y2 x-3 = 1/x3 Pythagorean Theorem The theorem that relates the three sides of a right triangle: a2 + b2 = c 2 a and b are the lengths of the two sides of the triangle that form the right angle. c is the third side of the triangle which is known as the hypotenuse. c The length of any side of right triangle can be found if you know the lengths of the other two sides, and you use the Pythagorean Theorem: a a2 + b2 = c 2 Remember, this only works for right triangles. b Example: If side a equals 4 and side b equals 3, what is the length of side c? a=4 c 4 3 b=3 Using the Pythagorean Theorem: a2 + b2 = c 2 ↓ (4) 2 + (3) 2 = c 2 ↓ 16 + 9 = c 2 c 2 = 25 ↓ c =5 c=?