{"id":11099,"date":"2021-04-20T18:26:37","date_gmt":"2021-04-20T12:56:37","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=11099"},"modified":"2021-09-15T11:33:32","modified_gmt":"2021-09-15T06:03:32","slug":"ap-board-7th-class-maths-solutions-chapter-11-intext-questions","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-7th-class-maths-solutions-chapter-11-intext-questions\/","title":{"rendered":"AP Board 7th Class Maths Solutions Chapter 11 Exponents InText Questions"},"content":{"rendered":"

AP State Syllabus\u00a0AP Board 7th Class Maths Solutions<\/a> Chapter 11 Exponents InText Questions and Answers.<\/p>\n

AP State Syllabus 7th Class Maths Solutions 11th Lesson Exponents InText Questions<\/h2>\n

\"AP<\/p>\n

Do This<\/span><\/p>\n

Question 1.
\nWrite the following in exponential form, (values are rounded off) (Page No. 212)
\ni) Total surface area of the Earth is 510,000,000 square kilometers.
\nSolution:
\n51 \u00d7 107<\/sup> = 3\u00d7 17 \u00d7 107<\/sup><\/p>\n

ii) Population of Rajasthan is approximately 7,00,00,000.
\nSolution:
\n7 \u00d7 107<\/sup><\/p>\n

iii) The approximate age of the Earth is 4550 million years.
\nSolution:
\n4550 millions = 4550 \u00d7 10,00,000 (v 1 million =10 lakhs)
\n= 455 \u00d7 107<\/sup> = 91 \u00d7 5 \u00d7 107<\/sup> = 5 \u00d7 7 \u00d7 13 \u00d7 107<\/sup><\/p>\n

iv) 1000 km in meters.
\nSolution:
\n1 km = 1000 m
\n\u2234 1000 km = 1000 \u00d7 1000 m = 106<\/sup><\/p>\n

\"AP<\/p>\n

Question 2.
\nExpress (i) 48951 (ii) 89325 in expanded form using exponents. (Page No. 212)
\nSolution:
\ni) 48951 = (4 \u00d7 10000) + (8 \u00d7 1000) + (9 \u00d7 100) + (5 \u00d7 10) + (1 \u00d7 1)
\n= (4 \u00d7 104) + (8\u00d7 103) + (9 \u00d7 102) + (5 \u00d7 1.0) + (1 \u00d7 1)<\/p>\n

ii) 89325 = (8 \u00d7 10000) + (9 \u00d7 1000) + (3 \u00d7 100) + (2 \u00d7 10) + (5 \u00d7 1)
\n= (8 \u00d7 104<\/sup>) + (9 \u00d7 103<\/sup>) + (3 \u00d7 102<\/sup>) + (2 \u00d7 10) + (5 \u00d7 1)<\/p>\n

Question 3.
\nIs 32<\/sup> equal to 23<\/sup> ? Justify. (Page No. 213)
\nSolution:
\n32<\/sup> \u2260 23<\/sup>
\nSince 32<\/sup> = 3 \u00d7 3 = 9 and 23<\/sup> = 8
\n\u2234 32<\/sup> \u2260 23<\/sup><\/p>\n

Question 4.
\nWrite the following numbers in exponential form. Also state the
\na) base b) exponent and c) how it is read.
\ni) 32 ii) 64 iii) 256 iv) 243 v) 49 (Page No. 213)
\nSolution:
\ni) 32 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 25<\/sup>
\nBase = 2; exponent = 5; read as 2 raised to the power 5.
\nii) 64 = 2 \u00d7 2\u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 26<\/sup>
\nBase = 2; exponent = 6 and we read it as 2 raised to the power 6.
\niii) 256 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 28<\/sup>
\nBase = 2, exponent = 8 and we read it as 2 raised to the power 8.
\niv) 243 = 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 = 35<\/sup>
\nBase = 3; exponent = 5 and we read it as 3 raised to the power 5.
\nv) 49 = 7 \u00d7 7 = 72<\/sup>
\n= 7 is the base ; exponent = 2.<\/p>\n

\"AP<\/p>\n

Question 5.
\nWrite the expanded form of the following. (Page No. 213)
\ni) p7<\/sup> ii) l4<\/sup> iii) s9<\/sup> iv) d6<\/sup> v) z5<\/sup>
\nSolution:
\ni) p7<\/sup> = p \u00d7 p \u00d7 p \u00d7 p \u00d7 p \u00d7 p \u00d7 p
\nii) l4<\/sup> = l \u00d7 l \u00d7 l \u00d7 l
\niii) s9<\/sup> = s \u00d7 s \u00d7 s \u00d7 s \u00d7 s \u00d7 s \u00d7 s \u00d7 s \u00d7 s
\niv) d6<\/sup> = d \u00d7 d \u00d7 d \u00d7 d \u00d7 d \u00d7 d
\nv) z5<\/sup> = z \u00d7 z \u00d7 z \u00d7 z \u00d7 z<\/p>\n

Question 6.
\nWrite the following in exponential form. (Page No. 213)
\ni) a \u00d7 a \u00d7 a \u00d7 ………………….l’ times
\nii) 5 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 ……………..\u2019n’ times
\niii) q \u00d7 q \u00d7 q \u00d7 q \u00d7 q ………………….15 times
\niv) r \u00d7 r \u00d7 r \u00d7 ………………….’b’ times
\nSolution:
\ni) a \u00d7 a \u00d7 a \u00d7 ………………….’l’ times = al<\/sup>
\nii) 5 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 ……………..\u2019n’ times = 5n<\/sup>
\niii) q \u00d7 q \u00d7 q \u00d7 q \u00d7 q …………….15 times = q15<\/sup>
\niv) r \u00d7 r \u00d7 r \u00d7 ……………..’b’ times = rb<\/sup><\/p>\n

Do This<\/span><\/p>\n

Question 1.
\nFind the values of 24<\/sup>, 23<\/sup> and 27<\/sup> and verify whether 24<\/sup> \u00d7 23<\/sup> = 27<\/sup>. (Page No. 215)
\n24<\/sup> = 2 \u00d7 2 \u00d7 2 \u00d72 = 16;
\n23<\/sup> = 2 \u00d7 2 x 2 = 8
\n27<\/sup> = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2\u00a0 \u00d7 2 = 128
\n24<\/sup> \u00d7 23<\/sup> = 16 \u00d7 8 = 128 = 27<\/sup>
\n24<\/sup> \u00d7 23<\/sup> = 27<\/sup><\/p>\n

Question 2.
\nFind the values of 52<\/sup>, 53<\/sup> and 55<\/sup> and verify whether 52<\/sup> \u00d7 53<\/sup> = 55<\/sup>. (Page No. 215)
\nSolution:
\n52<\/sup> = 5 \u00d7 5 = 25;
\n53<\/sup> = 5 \u00d7 5 \u00d7 5 = 125 and 55<\/sup> = 5 \u00d7 5 \u00d7 5 \u00d7 5 \u00d7 5 = 3125
\nNow 52 \u00d7 53 = 25 \u00d7 125 = 3125 = 55
\n\u2234 52<\/sup> \u00d7 53<\/sup> = 55<\/sup><\/p>\n

\"AP<\/p>\n

Question 3.
\nSimplify the following using the formula am<\/sup> \u00d7 an<\/sup> = am + n <\/sup>(Page No. 216)
\ni) 311<\/sup> \u00d7 39<\/sup> ii) p5<\/sup> \u00d7 p8<\/sup>
\nSolution:
\ni) 311<\/sup> \u00d7 39<\/sup> = 311+9<\/sup> = 320<\/sup>
\nii) p5<\/sup> \u00d7 p8<\/sup> = p5+8<\/sup> = p13<\/sup><\/p>\n

Question 4.
\nFind the appropriate number in place of the symbol’?’in the following. (Page No. 216)
\nLet ‘k’ be any non-zero integer.
\ni) k3<\/sup> \u00d7 k4<\/sup> = k?<\/sup>
\nSolution:
\ni) k3<\/sup> \u00d7 k4<\/sup> = k?<\/sup>
\nas k3<\/sup> \u00d7 k4<\/sup> = k3+4<\/sup> = k7<\/sup> the value of ‘?’ = 7<\/p>\n

ii) k15<\/sup> \u00d7 k?<\/sup> = k31<\/sup>
\nas k15<\/sup> \u00d7 k?<\/sup> = k15+?<\/sup>
\nbut k15 + ?<\/sup> = k31<\/sup>
\nSince bases are equal we equate the exponents
\n\u2234 15 + ? = 31
\n(i.e\u201e) ? = 31 – 15 = 16<\/p>\n

\"AP<\/p>\n

Question 5.
\nCompute 36<\/sup>, cube of 32<\/sup> and verify whether (32<\/sup>)3<\/sup> = 36<\/sup>. (Page No. 216)
\nSolution:
\n36<\/sup> = 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 = 729.
\ncube of 32<\/sup> = (32<\/sup>)3<\/sup> = 93<\/sup> = 9 \u00d7 9 \u00d7 9 = 729
\nNow (32<\/sup>)3<\/sup> = 32<\/sup> \u00d7 32<\/sup> \u00d7 32<\/sup> = 9 \u00d7 9 \u00d7 9 = 729
\n36<\/sup> = 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 = 9 \u00d7 9 \u00d7 9
\n(32<\/sup>)3<\/sup> = 36<\/sup><\/p>\n

Question 6.
\nSimplify the following using the law am<\/sup> \u00d7 bm<\/sup> = (ab)m\u00a0 <\/sup>(Page No. 218)
\ni) (2 \u00d7 3)4<\/sup>
\nii) xp<\/sup> \u00d7 yp<\/sup>
\niii) a8<\/sup> \u00d7 b8<\/sup>
\niv) (5 \u00d7 4)11<\/sup>
\nSolultion:
\ni) (2 \u00d7 3)4<\/sup> = 24<\/sup> \u00d7 3 4<\/sup> = (2 \u00d7 2 \u00d7 2 \u00d7 2) \u00d7 (3 \u00d7 3 \u00d7 3 \u00d73) = 16 \u00d7 81 = 1296
\nii) xp<\/sup> \u00d7 yp<\/sup> = (x . y)p<\/sup>
\niii) a8<\/sup> \u00d7 b8<\/sup> = (a.b)8<\/sup>
\niv) (5 \u00d7 4)11<\/sup> = 511<\/sup> \u00d7 411<\/sup> = 511<\/sup> \u00d7 (2 \u00d7 2)11<\/sup>
\n= 511<\/sup> \u00d7 211<\/sup> \u00d7 211<\/sup> = (5 \u00d7 2)11<\/sup> \u00d7 211<\/sup> = 1011<\/sup> \u00d7 211<\/sup><\/p>\n

\"AP<\/p>\n

Question 7.
\nWrite the following, by using \\(\\mathbf{a}^{-n}=\\frac{1}{\\mathbf{a}^{n}}\\) with positive exponents. (Page No. 219)
\nSolution:
\n\"AP
\n\"AP<\/p>\n

Question 8.
\nSimplify and write in the form of am-n<\/sup> or \\(\\frac{1}{\\mathbf{a}^{\\mathbf{n}-\\mathbf{m}}}\\)
\ni) \\(\\frac{13^{8}}{13^{5}}\\)
\nii) \\(\\frac{3^{4}}{3^{14}}\\)
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 9.
\nFill the appropriate number in the box. (Page No. 222)
\n\"AP
\nSolution:
\n\"AP<\/p>\n

Question 10.
\nComplete the following (Page No. 223)
\n\"AP
\nSolution:
\n\"AP<\/p>\n

Question 11.
\nWrite in expanded form. (Page No. 224)
\ni) a-5<\/sup>
\nii) (-a)4<\/sup>
\niii) (-7)-5<\/sup>
\niv) (-a)m<\/sup>
\nSolution:
\n\"AP
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 12.
\nWrite in exponential form. (Page No. 224)
\ni) (-3) \u00d7 (-3) \u00d7 (-3)
\nii) (-b) \u00d7 (-b) \u00d7 (-b) \u00d7 (-b)
\niii) \\(\\left(\\frac{1}{-2}\\right) \\times\\left(\\frac{1}{-2}\\right) \\times\\left(\\frac{1}{-2}\\right)\\) ………………….’m’ times
\nSolution:
\ni) (-3) \u00d7 (-3) \u00d7 (-3) = (-3)3<\/sup>
\nii) (-b) \u00d7 (-b) \u00d7 (-b) \u00d7 (-b) = (-b)4<\/sup>
\niii) \\(\\left(\\frac{1}{-2}\\right) \\times\\left(\\frac{1}{-2}\\right) \\times\\left(\\frac{1}{-2}\\right)\\) ………………….’m’ times = \\(\\left(-\\frac{1}{2}\\right)^{m}\\) or (-2)-m<\/sup><\/p>\n

Do This <\/span><\/p>\n

Question 1.
\nWrite the following in exponential form using prime factorization. (Page – 214)
\ni) 2500 ii) 1296 iii) 8000 iv)6300
\nSolution:
\ni) 2500 = 2 \u00d7 1250 = 2 \u00d7 2 \u00d7 625
\n= (2 \u00d7 2) \u00d7 5 \u00d7 125
\n= (2 \u00d7 2) \u00d7 5 \u00d7 5 \u00d7 25
\n= (2 \u00d7 2) \u00d7 (5 \u00d7 5 \u00d7 5 \u00d7 5)
\n= 22<\/sup> \u00d7 54<\/sup>
\n\"AP<\/p>\n

ii) 1296 = 2 \u00d7 648 = 2 \u00d7 2 \u00d7 324 = 2 \u00d7 2 \u00d7 2 \u00d7 162
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2) \u00d7 81
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2 ) \u00d7 \u00a03 \u00d7 27
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2 ) \u00d7 3 \u00d7 3 \u00d7 9
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2 ) \u00d7 ( 3 \u00d7 3 \u00d7 3 \u00d7 3 )
\n= 24<\/sup> \u00d7 34<\/sup>
\n\"AP<\/p>\n

iii) 8000 = 2 \u00d7 4000 = 2 \u00d7 2 \u00d7 2000 = 2 \u00d7 2 \u00d7 2 \u00d7 1000
\n= 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 500
\n= 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 250
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2) \u00d7 125
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2) \u00d7 5 \u00d7 25
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2) \u00d7 ( 5 \u00d7 5 \u00d7 5)
\n= (26<\/sup> \u00d7 53<\/sup>)
\n\"AP<\/p>\n

\"AP<\/p>\n

iv) 6300 = 2 \u00d7 3150 = 2 \u00d7 2 \u00d7 1575
\n= (2 \u00d7 2) \u00d7 3 \u00d7 525
\n= 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 175
\n= (2 \u00d7 2) \u00d7 (3 \u00d7 3) \u00d7 5 \u00d7 35
\n= (2 \u00d7 2) \u00d7 (3 \u00d7 3) \u00d7 (5 \u00d7 5) \u00d7 7
\n= 22<\/sup> \u00d7 32<\/sup> \u00d7 52<\/sup> \u00d7 7
\n\"AP<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus\u00a0AP Board 7th Class Maths Solutions Chapter 11 Exponents InText Questions and Answers. AP State Syllabus 7th Class Maths Solutions 11th Lesson Exponents InText Questions Do This Question 1. Write the following in exponential form, (values are rounded off) (Page No. 212) i) Total surface area of the Earth is 510,000,000 square kilometers. …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[9],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/11099"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=11099"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/11099\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=11099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=11099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=11099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}