Basic_Math_review_for_Comm_308

Basic_Math_review_for_Comm_308 - Exponents Exponents are a...

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1 Exponents: Exponents are a shorthand way of representing repeated multiplication. For example: x 3 = x*x*x 8 = 2*2*2 = 2 3 (-2) 3 = -8 = (-2)(-2)(-2) Laws of Exponents 1. x n x m = x n + m example: 4x 2 2x 3 8x -4 = (2 3 ) 2 4*2*8*x 2 x 3 x -4 = 2 6 4*2*8*x 2+3-4 = 64 4*2*8*x 1 = 64 64x = 64 x = 1 *********************** 2. x n x m = x n ± m 3. x n y n = xy () n 4. x n y n = x y ± ² ³ ´ µ n 5. x ± n = 1 x n 6. x n m = x nm 7. 1 n = 1 8. x 0 = 1 9. 0 n = 0 , except 0 0 = undefined
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2 Example: x 4 y 3 y 5 x 2 = 1 4 , x y = ? Using the laws of exponent: x 4 y 3 y 5 x 2 = x 4 x 2 ± y 3 y 5 = x 4 ² 2 y 5 ² 3 = x 2 y 2 = 1 2 2 ³ x y = 1 2 Examples: 1. Solve for x, x 5 -32 = 0 Isolate the x 5 term: x 5 = 32 (add 32 to both sides) Exponentiate both sides by (1/5). (x 5 ) (1/5) = (x 5/5 ) = 32 (1/5) Since 32 = 2 5 , you can simplify 32 (1/5) 32 (1/5) = (2 5 ) (1/5) Returning to the originally simplified expression: (x 5/5 ) = 32 (1/5) Or: x 1 = 2 (5/5) = 2 1 Therefore: x=2 2. Solve for x, (8 2x ) 2 = 64 x-2 Using laws of Exponent: (8 2x ) 2 =((8 2 ) x ) 2 =(64 2x ) = 64 x-2 Therefore: 2x=x-2 or: x=-2 ***********************
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3 Fractions: Numerator - The top number of a fraction. For example, in the fraction 2 / 5 , the numerator is 2. Denominator - The bottom number of a fraction. For example, in the fraction 2 / 5 , the denominator is 5. Mixed Fraction (aka Mixed Number) - The combination of a whole number and a proper fraction. For example, the fraction 1 3 / 8 is a mixed fraction since it combines a whole number (i.e., 1) and a proper fraction (i.e., 3 / 8 ). The Idea of a Fraction One way to understand a fraction is as a part of a whole. For example, the fraction 3/8 can be thought of as representing 3 pieces of pizza from an 8-piece pizza. Number Line Representation Since a fraction is a number, it occupies a place on the number line. Most fractions are not integers and as a result, they occupy a place on the number line between integers.
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Basic_Math_review_for_Comm_308 - Exponents Exponents are a...

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