\nVerify the general statement x-b<\/sup>=\\(\\frac{1}{x^{b}}\\) for x=3 and b=-5.
\nAnswer:
\nIf b were a positive integer, then we have what the definition states. However, b is a negative integer, specifically
\nb=-5, so the general statement in this case reads
\n3-(-5)<\/sup>=\\(\\frac{1}{3^{-5}}\\).
\nThe right side of this equation is
\n
![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-8-Module-1-Lesson-5-Exercise-Answer-Key-1.png\")
\nSince the left side is also 35<\/sup>, both sides are equal.
\n3-(-5)<\/sup>=\\(\\frac{1}{3^{-5}}\\)=35<\/sup><\/p>\n
Exercise 2. Exercise 3. Exercise 4. For Exercises 5\u201310, write an equivalent expression, in exponential notation, to the one given, and simplify as much as possible.<\/p>\n Exercise 5. Exercise 6. Exercise 7. Exercise 8. Exercise 9. Exercise 10. Exercise 11. Exercise 12. Exercise 13. Exercise 14. Question 1. Question 2. Question 3. Question 4. Write each expression in a simpler form that is equivalent to the given expression.<\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Engage NY Eureka Math 8th Grade Module 1 Lesson 5 Answer Key Eureka Math Grade 8 Module 1 Lesson 5 Exercise Answer Key Exercise 1. Verify the general statement x-b= for x=3 and b=-5. Answer: If b were a positive integer, then we have what the definition states. However, b is a negative integer, specifically … 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\/80572"}],"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=80572"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80572\/revisions"}],"predecessor-version":[{"id":137631,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/80572\/revisions\/137631"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=80572"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=80572"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=80572"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nWhat is the value of (3\u00d710-2<\/sup>)?
\nAnswer:
\n(3\u00d710-2<\/sup>) = 3 \u00d7 \\(\\frac{1}{10^{2}}\\) = \\(\\frac{3}{10^{2}}\\) =0.03<\/p>\n
\nWhat is the value of (3\u00d710-5<\/sup>)?
\nAnswer:
\n(3\u00d710-5<\/sup>) = 3\u00d7\\(\\frac{1}{10^{5}}\\) = \\(\\frac{3}{10^{5}}\\) =0.00003<\/p>\n
\nWrite the complete expanded form of the decimal 4.728 in exponential notation.
\nAnswer:
\n4.728=(4\u00d7100<\/sup>)+(7\u00d710-1<\/sup>)+(2\u00d710-2<\/sup>)+(8\u00d710-3<\/sup>)<\/p>\n
\n5-3<\/sup>=
\nAnswer:
\n\\(\\frac{1}{5^{3}}\\)<\/p>\n
\n\\(\\frac{1}{8^{9}}\\) =
\nAnswer:
\n8-9<\/sup><\/p>\n
\n3\u22192-4<\/sup>=
\nAnswer:
\n3\u2219\\(\\frac{1}{2^{4}}\\) =\\(\\frac{3}{2^{4}}\\)<\/p>\n
\nLet x be a nonzero number.
\nx-3<\/sup>=
\nAnswer:
\n\\(\\frac{1}{x^{3}}\\)<\/p>\n
\nLet x be a nonzero number.
\n\\(\\frac{1}{x^{9}}\\) =x-9<\/sup><\/p>\n
\nLet x,y be two nonzero numbers.
\nxy-4 <\/sup>=
\nAnswer:
\nx\u2219\\(\\frac{1}{y^{4}}\\) = \\(\\frac{x}{y^{4}}\\)<\/p>\n
\n\\(\\frac{19^{2}}{19^{5}}\\) =
\nAnswer:
\n192-5<\/sup><\/p>\n
\n\\(\\frac{17^{16}}{17^{-3}}\\) =
\nAnswer:
\n1716<\/sup>\u00d7\\(\\frac{1}{17^{-3}}\\) =1716<\/sup>\u00d7173<\/sup>= 1716+3<\/sup><\/p>\n
\nIf we let b=-1 in (11), a be any integer, and y be any nonzero number, what do we get?
\nAnswer:
\n(y-1<\/sup>)a<\/sup>=y-a<\/sup><\/p>\n
\nShow directly that (\\(\\frac{7}{5}\\))-4<\/sup>=\\(\\frac{7^{-4}}{5^{-4}}\\).
\nAnswer:
\n(\\(\\frac{7}{5}\\))-4<\/sup>=(7\u2219\\(\\frac{1}{5}\\))-4<\/sup> By the product formula
\n=(7\u22195-1<\/sup> )-4<\/sup> By definition
\n=7-4<\/sup>\u2219(5-1<\/sup> )-4<\/sup> By (xy)a<\/sup>=xa<\/sup> ya<\/sup> (12)
\n=7-4<\/sup>\u221954<\/sup> By (xb<\/sup> )a<\/sup>=xa<\/sup>b (11)
\n=7-4<\/sup>\u2219\\(\\frac{1}{5-4<\/sup>}\\) By x-b<\/sup>=\\(\\frac{1}{x^{b}}\\)(9)
\n=\\(\\frac{7^{-4}}{5^{-4}}\\) By product formula<\/p>\nEureka Math Grade 8 Module 1 Lesson 5 Problem Set Answer Key<\/h3>\n
\nCompute: 33<\/sup> \u00d732<\/sup> \u00d731<\/sup> \u00d730<\/sup>\u00d73-1<\/sup> \u00d73-2<\/sup>=
\nAnswer:
\n33<\/sup> =27
\nCompute: 52<\/sup> \u00d751<\/sup> 0\u00d758<\/sup> \u00d750<\/sup>\u00d75-10<\/sup> \u00d75-8<\/sup> =52<\/sup> =25
\nCompute for a nonzero number, a: am<\/sup> \u00d7an<\/sup> \u00d7al<\/sup> \u00d7a-n<\/sup> \u00d7a-m<\/sup> \u00d7a-l<\/sup> \u00d7a0<\/sup>=
\nAnswer:
\na0<\/sup>=1<\/p>\n
\nWithout using (10), show directly that (17.6-1<\/sup> )8<\/sup> = 17.6-8<\/sup> .
\nAnswer:
\n(17.6-1<\/sup>)8<\/sup> =(\\(\\frac{1}{17.6}\\))8<\/sup> By definition
\n= \\(\\frac{1^{8}}{17.6^{8}}\\) By (\\(\\frac{x}{y}\\))n<\/sup> = \\(\\frac{x^{n}}{y^{n}}\\) (5)
\n= \\(\\frac{1}{17.6^{8}}\\)
\n= 17.6-8<\/sup> By definition<\/p>\n
\nWithout using (10), show (prove) that for any whole number n and any nonzero number y, (y-1<\/sup> )n<\/sup> =y-n<\/sup> .
\nAnswer:
\n(y-1<\/sup> )n<\/sup> =(\\(\\frac{1}{y}\\))n<\/sup> By definition
\n=\\(\\frac{1^{n}}{y^{n}}\\) By (\\(\\frac{x}{y}\\))n<\/sup> = \\(\\frac{x^{n}}{y^{n}}\\)(5)
\n= \\(\\frac{1}{y^{n}}\\)
\n= y-n<\/sup> By definition<\/p>\n
\nWithout using (13), show directly that \\(\\frac{2.8^{-5}}{2.8^{7}}\\) = 2.8-12<\/sup> .
\nAnswer:
\n\\(\\frac{2.8^{-5}}{2.8^{7}}\\) = 2.8-5<\/sup> \u00d7 \\(\\frac{1}{2.8^{7}}\\) By the product formula for complex fractions
\n= \\(\\frac{1}{2.8^{5}}\\) \u00d7 \\(\\frac{1}{2.8^{7}}\\) By definition
\n= \\(\\frac{1}{2.8^{5} \\times 2.8^{7}}\\) By the product formula for complex fractions
\n= \\(\\frac{1}{2.8^{5+7}}\\) By xa<\/sup>\u2219xb<\/sup> =xa+b<\/sup> (10)
\n= \\(\\frac{1}{2.8^{12}}\\)
\n= 2.8-12<\/sup> By definition<\/p>\nEureka Math Grade 8 Module 1 Lesson 5 Exit Ticket Answer Key<\/h3>\n
\n76543-4<\/sup>=
\nAnswer:
\n\\(\\frac{1}{76543^{4}}\\)<\/p>\n
\nLet f be a nonzero number. f-4<\/sup>=
\nAnswer:
\n\\(\\frac{1}{f^{4}}\\)<\/p>\n
\n671\u00d728796-1<\/sup> =
\nAnswer:
\n671\u00d7\\(\\frac{1}{28796}\\)=\\(\\frac{671}{28796}\\)<\/p>\n
\nLet a, b be numbers (b\u22600). ab-1<\/sup> =
\nAnswer:
\na\u2219\\(\\frac{1}{b}\\)=\\(\\frac{a}{b}\\)<\/p>\n
\nLet g be a nonzero number. \\(\\frac{1}{g^{-1}}\\) =
\nAnswer:
\ng<\/p>\n","protected":false},"excerpt":{"rendered":"