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Chapter 1 Mid-Chapter Test Study Guide Scheduled for: Tuesday, January 24th Topics on Test: -Multiplying & Dividing Monomials (Lesson 3) -Powers of Monomials (Lesson 4) -Negative Exponents (Lesson 5) Laws of Exponents Law #1 Multiplying Monomials When we are multiplying numbers or variables with the SAME BASES we ADD the exponents Examples 26 • 25= 25+6=11 = 211 b³ • b² = b³+²= b5 3x³•y²•x3= 3x6y² (4x²)(3x³) = 12x5 MULTIPLY THE WHOLE NUMBERS then add exponents! Law #2 Dividing Monomials When we are dividing numbers or variables with the SAME BASES we subtract the exponents Example x6 t5 x3 t4 = x3t1 or x3t (either answer is fine!) Examples 25s3 x5 5s2 x4 = 5s1x1 or 5sx (either answer is fine!) 42 m6 x 7 m4 x = 6m2 **Where did the “x” go? Remember no exponent you plug in and 1 - 1= 0 1 for each variable Law #3 Power to Power When we are working with a power to a power we multiply the exponents Example (72)3 = 76 or 117,649 (d7)6 = d42 Law #4 Product to Power When we are working with a product to a power we apply the power to EACH factor (including any integers in the problem) and then multiply each. Example (7a5b6)4 = 74a20b24 = 2,401a20b24 (-3w3z8)5 = -35w15z40 = -243w15z40 Negative Exponents Write using Positive Exponents If a number is being raised to a negative exponent, move it in to the denominator to become a positive exponent. More Examples: 4-5 = m-9 = (-2)-6 = Evaluating Negative Exponents Solve out and write using a positive exponent Examples: (-5)-5 = - 3-2 = (-9)-4 = More with Negative Exponents To write this expression using negative exponents, bring the number t that is in the denominator up to the numerator and make it negative It will now be: 5-2 Rewrite the denominator using an exponent that is not 1. 36=62. So now the fraction is . Then move it back up and change the sign to be a negative. So the answer is 6-2. Multiplying and Dividing with Negative Exponents Step 1: Follow Law #1 (if multiplying) or Law #2 (if dividing) Step 2: If your exponent is POSITIVE leave your answer alone! If your exponent is NEGATIVE flip the fraction to make it a positive! Examples: 2-6 23 = 2-3 = (FLIP) (-6 + 3 = -3) s-5 s7 = s2 (LEAVE ALONE) (-5 + 7 = 2) Y-3 Y3 = Y0 = 1 (-3 + 3 = 0) = m12 (LEAVE ALONE) [8 – (-4) = 12] = 6-12 = [(-4) – 8 = -12] (FLIP)