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 Powers and Exponents 1 What Are You Learning? • • • I CAN write powers as a product of the same factor and I CAN write products in exponential form. I CAN evaluate exponents. 2 Why Do You Need To Know This? Exponents are used in the real-world to represent extremely large and small numbers. They are also used in solving problems. 3 Vocabulary Words Factors—Two or more numbers multiplied together to form a product. Example—2 • 3 = 6 The numbers 2 and 3 are factors. 4 Vocabulary Exponent—Number that tells how many times the base is used as a factor. 4²--2 is the exponent and it shows that 4 will be multiplied two times. 4 • 4 5 Vocabulary Base—The common factor or number being multiplied. 5•5•5•5•5 Five is the base 6 Vocabulary Powers—Numbers expressed using exponents 4² and 6³ are examples of powers. 4² is read “four to the second power.” 6³ is read “six to the third power.” 7 Vocabulary Squared—A number multiplied by itself two times. 4 x 4 or 4² The four is being squared. Cubed—A number multiplied by itself three times. 2 x 2 x 2 or 2³ 8 Write Numbers in Exponential Form Exponential Form—Numbers written with exponents. Example 1—Write (-5)(-5)(-5) in exponential form. -5 is the base. It is used as a factor 3 times. So, the exponent is 3. (-5)(-5)(-5) = (-5)³ 9 Write each expression in exponential form. a. 6·6·6 e. 9 · (p + 1)(p +1) b. (-3)(-3)(-3)(-3) f. -5 · x · x · y · y · x c. (-4n)(-4n)(-4n)(-4n)(-4n) g. (a + 1)(a +1)(a +1) d. 4·y·x·y·3·x·y 10 Write each expression in exponential form. -8 • n • n • n • 4 • t 25% 25% 25% 25% 1 2 3 4 5 6 7 8 9 10 11 12 13 21 22 23 24 25 26 27 28 29 30 31 32 33 14 2n t3 + -3 n3 -3 2 -3 •3 n 2n 3t 4. -8 3. •t 2. 4t -32n3t -32 • 3n • t -8n3 + 4t -32nt3 1. 15 16 17 18 19 20 11 Vocabulary Evaluate—Find the value of an expression. Standard Form—Numbers written without exponents. 12 Write Powers in Standard Form Evaluate each expression. Example 1 -- 2 to the fifth power = 2 · 2 · 2 · 2 · 2 = 32 Example 2-- 4³ = 4 · 4 · 4 = 64 13 Evaluate each expression. 7³ e. 3 · 4² b. 52 f. 4² · 5³ c. (-4)³ g. 2³ · 5² · 7 d. -8² h. 3 · 5² + 2³ · 3² a. 14 Evaluate. 2 -3 25% 25% 25% 25% -9 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 21 22 23 24 25 26 27 28 29 30 31 32 33 14 15 16 -6 3. 6 2. 9 -9 9 6 -6 1. 17 18 19 20 15 Evaluate each expression a. 5² · 8² · 3³ b. 9 · 6² · 2 · 3³ c. 3(2 • 2 + 5)² d. 6² + 2(6) + 5 16 Evaluate. 2 12 - 4 25% 25% 25% 25% -4 12 – 4 • 4 4 12 - 16 1. 2. 3. 4. -4 12 1 2 3 4 5 6 7 8 9 10 11 12 13 21 22 23 24 25 26 27 28 29 30 31 32 33 14 – 4 •4 15 4 12 16 17 -1 6 18 19 20 17 Determine whether each pair of expression is equivalent. Write yes or no. a. 4ab2 and 4(ab)2 b. (2x)³ and 8x³ c. (mn)4 and m4 • n4 d. c³d³ and cd³ 18 Compare using <, >, or =. a. 3³ 5² f. 35 b. 4³ 8² g. -10³ c. 64÷8 2³ h. 5² 23 d. 4•10 102 i. 6³ 42 e. -5³ j. 24 4² -3° 4³ (-10)³ 19 Class Work 20