Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Pre-Algebra Chapter 4 Study Guide Name _______________ Exponents show repeated multiplication. x3 = x • x • x 25 = 2 • 2 • 2 • 2 • 2 A negative sign in front of a term means “the opposite of” -(4)2 = - 16 If the negative sign is inside the parenthesis, as in (-4)2 , it means (-4)(-4) = 16 The order of operations states that you must work inside the parenthesis before raising to a power. Remember PEMDAS 25 + 2(1 + 5)2 25 + 2(6)2 = 25 + 2(36) 25 + 72 = 97 3(6-4)3 3(2)3 = 3(8) = 24 Evaluate (x + y)3 for x = 3 and y = -6 (3 + -6)3 = (-3)3 = -27 Use prime factorization to find the greatest common factor (GCF) of two numbers. Remember that factors are small. With variables, use the smallest exponent of each variable that both terms have in common. 56 = 2 • 2• 2 • 7 42 = 2 • 3 • 7 Their GCF is 2 • 7 which is 14. Find the GCF of 64 and 48. (Use the cake method) 16 Find the GCF of 28xy7 and 32x2y4 (Use the cake method for the coefficients) 4xy4 Two numbers are relatively prime if their GCF is 1. The numbers by themselves may not be prime, but compared to each other, they have no factors in common. All numbers have 1 as a factor. You can find equivalent fractions by multiplying or dividing the numerator and denominator by the same nonzero factor. A fraction is in simplest form when the numerator and denominator have no common factors other than 1. p 2p divide the numerator and denominator by the common factor, p p =1 2p 2 Simplify 3ab2 12ac b2 4c 42 + 2(-3) 5 28 35 16 + -6 5 10 5 4 5 2 1 x5 x5 6 18x0 3 Evaluate each expression for a = -4 and b = -3 b a 3 4 b–a a–b -3 - -4 -4 - -3 -1 b2 a2 9 16 To multiply numbers with the same base, add the exponents. To divide numbers with the same base, subtract the exponents. To find a power of a power, multiply the exponents. x5 • x2 • y4 • y-2 = x7y2 38 35 33 x6y5 x3y3 x3y2 (23)4 = 212 (x5)6 x30 14rs3 8r2st 7s2 4rt Scientific notation is the product of two factors, a decimal greater than or equal to 1, and a power of 10. Big numbers have positive exponents, and small numbers have negative exponents. 458,000,000 = 4.58 x 108 0.0000007 = 7.0 x 10-7 Write in scientific notation 0.0004531 4.531 x 10-4 72,430,000 7.243 x 107 207,500 2.075 x 105 .00008524 8.524 x 10-5 Write in standard notation 3.21 x 107 32,100,000 5.9 x 10-8 .000000059 7.423 x 108 742,300,000 9.01 x 10-2 .0901