{"id":17552,"date":"2022-02-22T11:10:07","date_gmt":"2022-02-22T05:40:07","guid":{"rendered":"https:\/\/apboardsolutions.com\/?p=17552"},"modified":"2023-03-30T12:22:41","modified_gmt":"2023-03-30T06:52:41","slug":"ap-board-8th-class-maths-solutions-chapter-4-ex-4-1-in-telugu","status":"publish","type":"post","link":"https:\/\/apboardsolutions.com\/ap-board-8th-class-maths-solutions-chapter-4-ex-4-1-in-telugu\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 4 \u0c18\u0c3e\u0c24\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 \u0c18\u0c3e\u0c24\u0c3e\u0c32\u0c41 Ex 4.1"},"content":{"rendered":"

SCERT AP 8th Class Maths Solutions<\/a> Chapter 4 \u0c18\u0c3e\u0c24\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 \u0c18\u0c3e\u0c24\u0c3e\u0c32\u0c41 Ex 4.1 Textbook Exercise Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 4th Lesson \u0c18\u0c3e\u0c24\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 \u0c18\u0c3e\u0c24\u0c3e\u0c32\u0c41 Exercise 4.1<\/h2>\n

1. \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c1a\u0c3f \u0c24\u0c17\u0c41 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c41\u0c2a\u0c41\u0c2e\u0c41.
\n(i) 4-3<\/sup>
\n(ii) (-2)7<\/sup>
\n(iii) \\(\\left(\\frac{3}{4}\\right)^{-3}\\)
\n(iv) (-3)-4<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n(i) 4-3<\/sup> = \\(\\frac{1}{4^{3}}=\\frac{1}{64}\\)
\n[\u2235 \\(a^{-n}=\\frac{1}{a^{n}}\\)]<\/p>\n

(ii) (-2)7<\/sup> = – (2)7<\/sup> = – 128 [\u2235 7 \u0c2c\u0c47\u0c38\u0c3f\u0c38\u0c02\u0c16\u0c4d\u0c2f]
\n\u0c0e\u0c02\u0c26\u0c41\u0c15\u0c28\u0c17\u0c3e (-a)n<\/sup> \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c23\u0c32\u0c4b n \u0c2c\u0c47\u0c38\u0c3f\u0c38\u0c02\u0c16\u0c4d\u0c2f \u0c05\u0c2f\u0c3f\u0c28 (-a)n<\/sup> = – an<\/sup> \u0c05\u0c17\u0c41\u0c28\u0c41.<\/p>\n

(iii) \\(\\left(\\frac{3}{4}\\right)^{-3}\\)
\n\"AP<\/p>\n

(iv) (3)-4<\/sup> = \\(\\frac{1}{(-3)^{4}}\\) [\u2235 \\(a^{-n}=\\frac{1}{a^{n}}\\)]
\n= \\(\\frac{1}{3^{4}}\\) [\u2235 4 \u0c12\u0c15 \u0c38\u0c30\u0c3f\u0c38\u0c02\u0c16\u0c4d\u0c2f]
\n= \\(\\frac {1}{81}\\)<\/p>\n

\"AP<\/p>\n

2. \u0c15\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3e\u0c28\u0c3f\u0c28\u0c3f \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c2a\u0c41\u0c2e\u0c41.
\n(i) \\(\\left(\\frac{1}{2}\\right)^{4} \\times\\left(\\frac{1}{2}\\right)^{5} \\times\\left(\\frac{1}{2}\\right)^{6}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\\(\\left(\\frac{1}{2}\\right)^{4+5+6}=\\left(\\frac{1}{2}\\right)^{15}\\)
\n= \\(\\frac{1}{2^{15}}\\) [\u2235 am<\/sup> \u00d7 an<\/sup> = am+n<\/sup>]<\/span><\/p>\n

(ii) (-2)7<\/sup> \u00d7 (-2)3<\/sup> \u00d7 (-2)4<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n(-2)7+3+7<\/sup> = (-2)14<\/sup> = 214<\/sup>
\n[\u2235 (-a)n<\/sup> = an<\/sup>, n \u0c12\u0c15 \u0c38\u0c30\u0c3f\u0c38\u0c02\u0c16\u0c4d\u0c2f ]<\/p>\n

(iii) 44<\/sup> \u00d7 \\(\\left(\\frac{5}{4}\\right)^{4}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\\(4^{4} \\times \\frac{5^{4}}{4^{4}}=5^{4}\\)
\n[\u2235 \\(\\left(\\frac{a}{b}\\right)^{m}=\\frac{a^{m}}{b^{m}}\\)]<\/p>\n

(iv) \\(\\left[\\frac{5^{-4}}{5^{-6}}\\right] \\times 5^{3}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= 5-4<\/sup> \u00d7 (56<\/sup> \u00d7 53<\/sup>) [\u2235 \\(\\frac{1}{a^{-n}}=a^{n}\\)]
\n= 5-4<\/sup> \u00d7 56+3<\/sup> [\u2235 am<\/sup> \u00d7 an<\/sup> = am+n<\/sup>]
\n= 5-4<\/sup> \u00d7 59<\/sup> = 5(-4)+9 <\/sup>= 55<\/sup><\/p>\n

(v) (-3)4<\/sup> \u00d7 74<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= 34<\/sup> \u00d7 74<\/sup> [\u2235 4 \u0c12\u0c15 \u0c38\u0c30\u0c3f \u0c38\u0c02\u0c16\u0c4d\u0c2f ]
\n= (3 \u00d7 7)4<\/sup> = (21)4<\/sup> [\u2235 am<\/sup> \u00d7 bm<\/sup> = (ab)m<\/sup>]<\/p>\n

3. \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c2a\u0c41\u0c2e\u0c41.
\n(i) \\(2^{2} \\times \\frac{3^{2}}{2^{-2}} \\times 3^{-1}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= 22<\/sup> \u00d7 22<\/sup> \u00d7 32<\/sup> \u00d73-1<\/sup> [\u2235 \\(\\frac{1}{a^{-n}}=a^{n}\\)]
\n= 22+2 <\/sup>\u00d7 32+(-1)<\/sup>
\n= 24<\/sup> \u00d7 31<\/sup> = 16 \u00d7 3 = 48<\/p>\n

(ii) (4-1<\/sup> \u00d7 3-1<\/sup>) \u00f7 6-1<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= \\(\\left(\\frac{1}{4} \\times \\frac{1}{3}\\right) \\div \\frac{1}{6}\\) [\u2235 \\(a^{-n}=\\frac{1}{a^{n}}\\)]
\n= \\(\\frac{1}{12}+\\frac{1}{6}\\)
\n= \\(\\frac {6}{12}\\)
\n= \\(\\frac {1}{2}\\)
\n= 2-1<\/sup><\/p>\n

\"AP<\/p>\n

4. \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c1a\u0c3f \u0c24\u0c17\u0c41 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c2a\u0c02\u0c21\u0c3f.
\n(i) (40<\/sup> + 5-1<\/sup>) \u00d7 52<\/sup> \u00d7 \\(\\frac {1}{3}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

(ii) \\(\\left(\\frac{1}{2}\\right)^{-3} \\times\\left(\\frac{1}{4}\\right)^{-3} \\times\\left(\\frac{1}{5}\\right)^{-3}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

(iii) (2-1<\/sup> + 3-1<\/sup> + 4-1<\/sup>) \u00d7 \\(\\frac {3}{4}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

(iv) \\(\\frac{3^{-2}}{3} \\times\\left(3^{0}-3^{-1}\\right)\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

(v) 1 + 2-1<\/sup> + 3-1<\/sup> + 40<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

(vi) \\(\\left[\\left(\\frac{3}{2}\\right)^{-2}\\right]^{2}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

\"AP<\/p>\n

5. \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c1a\u0c3f \u0c24\u0c17\u0c41 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c2a\u0c02\u0c21\u0c3f.
\n(i) \\(\\left[\\left(3^{2}-2^{2}\\right) \\div \\frac{1}{5}\\right]^{2}\\)
\n(ii) ((52<\/sup>)3<\/sup> \u00d7 54<\/sup>) \u00f7 56<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n(i) \\(\\left[\\left(3^{2}-2^{2}\\right) \\div \\frac{1}{5}\\right]^{2}\\)
\n= \\(\\left[5 \\times \\frac{5}{1}\\right]^{2}\\)
\n= (52<\/sup>)2<\/sup> = 54<\/sup> = 625 [\u2235 (am<\/sup>)n<\/sup> = amn<\/sup>]<\/p>\n

(ii) ((52<\/sup>)3<\/sup> \u00d7 54<\/sup>) \u00f7 56<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

6. \u0c15\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3e\u0c28\u0c3f\u0c32\u0c4b ‘n’ \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c28\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c41\u0c2e\u0c41.
\n(i) \\(\\left(\\frac{2}{3}\\right)^{3} \\times\\left(\\frac{2}{3}\\right)^{5}=\\left(\\frac{2}{3}\\right)^{n-2}\\)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP
\n\u0c2d\u0c42\u0c2e\u0c41\u0c32\u0c41 \u0c38\u0c2e\u0c3e\u0c28\u0c2e\u0c48\u0c28 \u0c18\u0c3e\u0c24\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41 \u0c38\u0c2e\u0c3e\u0c28\u0c3e\u0c32\u0c41.
\n\u21d2 n – 2 = 8 \u21d2 n = 8 + 2 = 10
\n\u2234 n = 10<\/p>\n

(ii) (-3)n+1<\/sup> \u00d7 (-3)5<\/sup> = (-3)-4<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n\u21d2 (-3)n+1+5<\/sup> = (-3)-4<\/sup> [\u2235 am<\/sup> x an<\/sup> = am+n<\/sup>]
\n\u21d2 (-3)n+6<\/sup> = (-3)-4<\/sup>
\n\u21d2 n + 6 = -4
\nn = – 4 – 6 = – 10
\n\u2234 n = – 10<\/p>\n

(iii) 72n+1 <\/sup>\u00f7 49 = 73<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

7. 2-3<\/sup> = \\(\\frac{1}{2^{x}}\\) \u0c05\u0c2f\u0c3f\u0c28 x \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c28\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c41\u0c2e\u0c41.
\n\u0c38\u0c3e\u0c27\u0c28.
\n2-3<\/sup> = \\(\\frac{1}{2^{x}}\\) = 2-x<\/sup> [\u2235 \\(\\frac{1}{a^{n}}=a^{-n}\\)]
\n\u21d2 2-3<\/sup> = 2-x<\/sup>
\n\u21d2 -x = -3
\n\u2234 x = 3<\/p>\n

\"AP<\/p>\n

8. \\(\\left[\\left(\\frac{3}{4}\\right)^{-2} \\div\\left(\\frac{4}{5}\\right)^{-3}\\right] \\times\\left(\\frac{3}{5}\\right)^{-2}\\) \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c1a\u0c41\u0c2e\u0c41.
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n

9. m = 3 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 n = 2 \u0c05\u0c2f\u0c3f\u0c28 \u0c08 \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3e\u0c28\u0c3f \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c28\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c41\u0c2e\u0c41.
\ni) 9m2<\/sup> – 10n3<\/sup>
\nii) am2<\/sup>n2<\/sup>
\niii) 2m3<\/sup> + 3n2<\/sup> – 5m2<\/sup>n
\niv) mn<\/sup> – nm<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\ni) 9m2<\/sup> – 10n3<\/sup> = 9(3)2<\/sup> – 10(2)3<\/sup>
\n= 9 \u00d7 9 – 10 \u00d7 8
\n= 81 – 80 = 1<\/p>\n

ii) 2m2<\/sup>n2<\/sup>
\n= 2(3)2<\/sup>(2)2<\/sup>
\n= 2 \u00d7 9 \u00d7 4
\n= 72<\/p>\n

iii) 2m3<\/sup> + 3n2<\/sup> – 5m2<\/sup>n
\n= 2(3)3<\/sup> + 3(2)2<\/sup> – 5(3)2<\/sup> \u00d7 2
\n= (2 \u00d7 27) + (3 \u00d7 4) – (5 \u00d7 9 \u00d7 2)
\n= 54 + 12 – 90
\n= 66 – 90
\n= – 24<\/p>\n

iv) mn<\/sup> – nm<\/sup> = 32<\/sup> – 23<\/sup>
\n= 3 \u00d7 3 – 2 \u00d7 2 \u00d7 2 = 9 – 8 = 1<\/p>\n

\"AP<\/p>\n

10. \\(\\left(\\frac{4}{7}\\right)^{-5} \\times\\left(\\frac{7}{4}\\right)^{-7}\\) \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c1a\u0c3f \u0c24\u0c17\u0c41 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c2a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n\"AP<\/p>\n","protected":false},"excerpt":{"rendered":"

SCERT AP 8th Class Maths Solutions Chapter 4 \u0c18\u0c3e\u0c24\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 \u0c18\u0c3e\u0c24\u0c3e\u0c32\u0c41 Ex 4.1 Textbook Exercise Questions and Answers. AP State Syllabus 8th Class Maths Solutions 4th Lesson \u0c18\u0c3e\u0c24\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 \u0c18\u0c3e\u0c24\u0c3e\u0c32\u0c41 Exercise 4.1 1. \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c1a\u0c3f \u0c24\u0c17\u0c41 \u0c15\u0c3e\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c41\u0c2a\u0c41\u0c2e\u0c41. (i) 4-3 (ii) (-2)7 (iii) (iv) (-3)-4 \u0c38\u0c3e\u0c27\u0c28. (i) 4-3 = [\u2235 ] (ii) (-2)7 = – (2)7 … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":36802,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"https:\/\/apboardsolutions.com\/wp-content\/uploads\/2022\/02\/Chapter-4-\u0c18\u0c3e\u0c24\u0c3e\u0c02\u0c15\u0c3e\u0c32\u0c41-\u0c2e\u0c30\u0c3f\u0c2f\u0c41-\u0c18\u0c3e\u0c24\u0c3e\u0c32\u0c41-Ex-4.1.png","_links":{"self":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17552"}],"collection":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/comments?post=17552"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17552\/revisions"}],"predecessor-version":[{"id":17553,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17552\/revisions\/17553"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media\/36802"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media?parent=17552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/categories?post=17552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/tags?post=17552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}