\nExample 1.
\n5 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 5 =
\nAnswer:
\n55<\/sup><\/p>\n
Example 2. Write each expression in expanded form. Example 4. Example 5. Go back to Examples 1 – 4, and use a calculator to evaluate the expressions.<\/p>\n Example 1. Example 2. Example 3. Example 4. Example 5. Example 6. Example 7. Example 8. The base number can also be a fraction. Convert the decimals to fractions in Examples 7 and 8 and evaluate. Leave your answer as a fraction. Remember how to multiply fractions!<\/p>\n Example 7. Example 8. Example 9. Example 10. Exercise 1. Answer:<\/p>\n Exercise 2. Exercise 3. Exercise 4. Question 1. Answer:<\/p>\n Question 2. Question 3. Question 4. Question 5. Question 6. a. Explain what w is in this new expression. b. Explain what b is in this new expression. Question 7. Question 8. Question 1. Question 2. Question 3. As you evaluate these expressions, pay attention to how you arrive at your answers.<\/p>\n Question 1. Question 2. Question 3. Progression of Exercises<\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Engage NY Eureka Math 6th Grade Module 4 Lesson 5 Answer Key Eureka Math Grade 6 Module 4 Lesson 5 Example Answer Key Write each expression in exponential form. Example 1. 5 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 5 = Answer: 55 Example 2. 2 \u00d7 2 \u00d7 2 \u00d7 2 = Answer: 24 … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85717"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=85717"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85717\/revisions"}],"predecessor-version":[{"id":137143,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85717\/revisions\/137143"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=85717"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=85717"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=85717"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n2 \u00d7 2 \u00d7 2 \u00d7 2 =
\nAnswer:
\n24<\/sup><\/p>\n
\nExample 3.
\n83<\/sup> =
\nAnswer:
\n8 \u00d7 8 \u00d7 8<\/p>\n
\n106<\/sup> =
\nAnswer:
\n10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10<\/p>\n
\ng3<\/sup> =
\nAnswer:
\ng \u00d7 g \u00d7 g<\/p>\n
\n5 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 5 = 55<\/sup>
\nAnswer:
\n3,125<\/p>\n
\n2 \u00d7 2 \u00d7 2 \u00d7 2 = 24<\/sup>
\nAnswer:
\n16<\/p>\n
\n83<\/sup> = 8 \u00d7 8 \u00d7 8
\nAnswer:
\n512<\/p>\n
\n106<\/sup> = 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10 \u00d7 10
\nAnswer:
\n1,000,000<\/p>\n
\nWhat is the difference between 3g and g3<\/sup>?
\nAnswer:
\n3g = g + g + g or 3 times g; g3<\/sup> = g \u00d7 g \u00d7 g<\/p>\n
\nWrite the expression in expanded form, and then evaluate.
\n(3.8)4<\/sup> =
\nAnswer:
\n3.8 \u00d7 3.8 \u00d7 3.8 \u00d7 3.8 = 208.5136<\/p>\n
\nWrite the expression in exponential form, and then evaluate.
\nAnswer:
\n2.1 \u00d7 2.1 = (2.1)2 <\/sup>= 4.41<\/p>\n
\nWrite the expression in exponential form, and then evaluate.
\n0.75 \u00d7 0.75 \u00d7 0.75
\nAnswer:
\n= (0.75)3<\/sup> = 0.421875<\/p>\n
\nAnswer:
\n\\(\\frac{21}{10} \\times \\frac{21}{10}=\\left(\\frac{21}{10}\\right)^{2}=\\frac{441}{100}=4 \\frac{41}{100}\\)<\/p>\n
\nAnswer:
\n\\(\\frac{3}{4} \\times \\frac{3}{4} \\times \\frac{3}{4}=\\left(\\frac{3}{4}\\right)^{3}=\\frac{27}{64}\\)<\/p>\n
\nWrite the expression in exponential form, and then evaluate.
\nAnswer:
\n\\(\\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2}=\\left(\\frac{1}{2}\\right)^{3}=\\frac{1}{8}\\)<\/p>\n
\nWrite the expression in expanded form, and then evaluate.
\nAnswer:
\n\\(\\left(\\frac{2}{3}\\right)^{2}=\\frac{2}{3} \\times \\frac{2}{3}=\\frac{4}{9}\\)<\/p>\nEureka Math Grade 6 Module 4 Lesson 5 Exercise Answer Key<\/h3>\n
\nFill in the missing expressions for each row. For whole number and decimal bases, use a calculator to find the standard form of the number. For fraction bases, leave your answer as a fraction.<\/p>\n\n\n
\n Exponential Form<\/td>\n Expanded Form<\/td>\n Standard Form<\/td>\n<\/tr>\n \n 32<\/sup><\/td>\n 3 \u00d7 3<\/td>\n 9<\/td>\n<\/tr>\n \n <\/td>\n 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/td>\n <\/td>\n<\/tr>\n \n 45<\/sup><\/td>\n <\/td>\n <\/td>\n<\/tr>\n \n <\/td>\n \\( \\frac{3}{4} \\times \\frac{3}{4} \\)<\/td>\n <\/td>\n<\/tr>\n \n <\/td>\n 1.5 \u00d7 1.5<\/td>\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \n\n
\n Exponential Form<\/td>\n Expanded Form<\/td>\n Standard Form<\/td>\n<\/tr>\n \n 32<\/sup><\/td>\n 3 \u00d7 3<\/td>\n 9<\/td>\n<\/tr>\n \n 26<\/sup><\/td>\n 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/td>\n 64<\/td>\n<\/tr>\n \n 45<\/sup><\/td>\n 4 \u00d7 4 \u00d7 4 \u00d7 4 \u00d7 4<\/td>\n 1,024<\/td>\n<\/tr>\n \n \\(\\left(\\frac{3}{4}\\right)^{2}\\)<\/td>\n \\( \\frac{3}{4} \\times \\frac{3}{4} \\)<\/td>\n \\( \\frac{9}{16} \\)<\/td>\n<\/tr>\n \n (1.5)2<\/sup><\/td>\n 1.5 \u00d7 1.5<\/td>\n 2.25<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\nWrite five cubed in all three forms: exponential form, expanded form, and standard form.
\nAnswer:
\n53<\/sup>; 5 \u00d7 5 \u00d7 5; 125<\/p>\n
\nWrite fourteen and seven-tenths squared in all three forms.
\nAnswer:
\n(14.7)2<\/sup>; 14.7 \u00d7 14.7; 216.09<\/p>\n
\nOne student thought two to the third power was equal to six. What mistake do you think he made, and how would you help him fix his mistake?
\nAnswer:
\nThe student multiplied the base, 2, by the exponent, 3. This is wrong because the exponent never multiplies the base; the exponent tells how many copies of the base are to be used as factors.<\/p>\nEureka Math Grade 6 Module 4 Lesson 5 Problem Set Answer Key<\/h3>\n
\nComplete the table by filling in the blank cells. Use a calculator when needed.<\/p>\n\n\n
\n Exponential Form<\/td>\n Expanded Form<\/td>\n Standard Form<\/td>\n<\/tr>\n \n 35<\/sup><\/td>\n <\/td>\n <\/td>\n<\/tr>\n \n <\/td>\n 4 \u00d7 4 \u00d7 4<\/td>\n <\/td>\n<\/tr>\n \n (1.9)2<\/sup><\/td>\n <\/td>\n <\/td>\n<\/tr>\n \n \\(\\left(\\frac{1}{2}\\right)^{5}\\)<\/td>\n <\/td>\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \n\n
\n Exponential Form<\/td>\n Expanded Form<\/td>\n Standard Form<\/td>\n<\/tr>\n \n 35<\/sup><\/td>\n 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3<\/td>\n 243<\/td>\n<\/tr>\n \n 43<\/sup><\/td>\n 4 \u00d7 4 \u00d7 4<\/td>\n 64<\/td>\n<\/tr>\n \n (1.9)2<\/sup><\/td>\n 1.9 \u00d7 1.9<\/td>\n 3.61<\/td>\n<\/tr>\n \n \\(\\left(\\frac{1}{2}\\right)^{5}\\)<\/td>\n \\( \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\times \\frac{1}{2} \\)<\/td>\n \\( \\frac{1}{32} \\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\nWhy do whole numbers raised to an exponent get greater, while fractions raised to an exponent get smaller?
\nAnswer:
\nAs whole numbers are multiplied by themselves, products are larger because there are more groups. As fractions of fractions are taken, the product is smaller. A part of a part is less than how much we started with.<\/p>\n
\nThe powers of 2 that are in the range 2 through 1,000 are 2, 4, 8, 16, 32, 64, 128, 256, and 512. Find all the powers of that are in the range 3 through 1,000.
\nAnswer:
\n3, 9, 27, 81, 243, 729<\/p>\n
\nFind all the powers of 4 in the range 4 through 1,000.
\nAnswer:
\n4, 16, 64, 256<\/p>\n
\nWrite an equivalent expression for n \u00d7 a using only addition.
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-6-Module-4-Lesson-5-Problem-Set-Answer-Key-1.png\")
<\/p>\n
\nWrite an equivalent expression for wb<\/sup> using only multiplication.
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Grade-6-Module-4-Lesson-5-Problem-Set-Answer-Key-2.png\")
<\/p>\n
\nAnswer:
\nw is the factor that will be repeatedly multiplied by itself.<\/p>\n
\nAnswer:
\nb is the number of times w will be multiplied.<\/p>\n
\nWhat is the advantage of using exponential notation?
\nAnswer:
\nIt is a shorthand way of writing a multiplication expression if the factors are all the same.<\/p>\n
\nWhat is the difference between 4x and x4<\/sup>? Evaluate both of these expressions when x = 2
\nAnswer:
\n4x means four times x; this is the same as x + x + x + x. On the other hand, x4<\/sup> means x to the fourth power, or x \u00d7 x \u00d7 x \u00d7 x.
\nWhen x = 2, 4x = 4 \u00d7 2 = 8.
\nWhen x = 2, x4<\/sup> = 2 \u00d7 2 \u00d7 2 \u00d7 2 = 16.<\/p>\nEureka Math Grade 6 Module 4 Lesson 5 Exit Ticket Answer Key<\/h3>\n
\nWhat is the difference between 6z and z6<\/sup>?
\nAnswer:
\n6z = z + z + z + z + z + z or 6 times z; z6<\/sup> = z \u00d7 z \u00d7 z \u00d7 z \u00d7 z \u00d7 z<\/p>\n
\nWrite 103<\/sup> as a multiplication expression having repeated factors.
\nAnswer:
\n10 \u00d7 10 \u00d7 10<\/p>\n
\nWrite 8 \u00d7 8 \u00d7 8 \u00d7 8 using an exponent.
\nAnswer:
\n84<\/sup><\/p>\nEureka Math Grade 6 Module 4 Lesson 5 Opening Exercise Answer Key<\/h3>\n
\n4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4
\nAnswer:
\n4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 4 \u00d7 10
\n= 410<\/sup><\/p>\n
\n9 + 9 + 9 + 9 + 9
\nAnswer:
\n9 + 9 + 9 + 9 + 9 = 9 \u00d7 5
\n= 95<\/sup><\/p>\n
\n10 + 10 + 10 + 10 + 10
\nAnswer:
\n10 + 10 + 10 + 10 + 10 = 10 \u00d7 5
\n= 105<\/sup><\/p>\nEureka Math Grade 6 Module 4 Lesson 5 Multiplication of Decimals Answer Key<\/h3>\n
\n0.5 \u00d7 0.5 =
\nAnswer:
\n0.25<\/p>\n
\n0.6 \u00d7 0.6 =
\nAnswer:
\n0.36<\/p>\n
\n0.7 \u00d7 0.7
\nAnswer:
\n0.49<\/p>\n
\n0.5 \u00d7 0.6 =
\nAnswer:
\n0.3<\/p>\n
\n1.5 \u00d7 1.5 =
\nAnswer:
\n0.25<\/p>\n
\n2.5 \u00d7 2.5 =
\nAnswer:
\n6.25<\/p>\n
\n0.25 \u00d7 0.25 =
\nAnswer:
\n0.0625<\/p>\n
\n0.1 \u00d7 0.1 =
\nAnswer:
\n0.01<\/p>\n
\n0.1 \u00d7 123.4 =
\nAnswer:
\n12.34<\/p>\n
\n0.01 \u00d7 123.4 =
\nAnswer:
\n1.234<\/p>\n","protected":false},"excerpt":{"rendered":"