Basic Engineering Mathematics, Fifth Edition

48 Basic Engineering Mathematics Problem 3. Evaluate 3^3 × 22 33 × 22 = 3 × 3 × 3 × 2 × 2 = 27 × 4 = 108 7.2.2 Square roots When ...

Powers, roots and laws of indices 49 (4) 3^0 =1 and 17^0 = 1 This is the fourth law of indices, which states that when a number ...

50 Basic Engineering Mathematics (b) ( 3 × 35 )÷( 32 × 33 )= 3 × 35 32 × 33 = 3 (^1 +^5 ) 3 (^2 +^3 ) = 36 35 = 36 −^5 = 31 = 3 ...

Powers, roots and laws of indices 51 Problem 17. Find the value of 23 × 35 ×( 72 )^2 74 × 24 × 33 23 × 35 ×( 72 )^2 74 × 24 × 33 ...

52 Basic Engineering Mathematics Dividing each term by the HCF (i.e. 2^2 )gives 28 × 3 −^4 22 × 33 − 23 = 26 × 3 −^4 33 − 2 = 26 ...

Chapter 8 Units, prefixes and engineering notation 8.1 Introduction Of considerable importance in engineering is a knowl- edge o ...

54 Basic Engineering Mathematics Table 8.2 Some quantities and their units that are common in engineering Quantity Unit Symbol L ...

Units, prefixes and engineering notation 55 Table 8.3Common SI multiples Prefix Name Meaning G giga multiply by 10^9 i.e.× 10000 ...

56 Basic Engineering Mathematics What does the prefix p mean? What is thesymbol and meaning ofthe prefix mega? 8.4 Standard fo ...

Units, prefixes and engineering notation 57 In problems 6 and 7, express the numbers given as integers or decimal fractions. (a ...

58 Basic Engineering Mathematics Hence, 42× 105 = 4. 2 × 106 in engineering notation =4.2 Min prefix form. (b) Enter 47÷ 1010 ...

Units, prefixes and engineering notation 59 Rewrite 0.003mA inμA Rewrite 2025kHz as MHz Rewrite 5× 104 NinkN Rewrite 300pF in n ...

Revision Test 3 : Ratio, proportion, powers,roots, indices andunits This assignment covers the material contained in Chapters 6– ...

Chapter 9 Basic algebra 9.1 Introduction We are already familiar with evaluating formulae using a calculator from Chapter 4. For ...

62 Basic Engineering Mathematics 9.2.1 Addition and subtraction Problem 1. Find the sum of 4x, 3 x,− 2 xand−x 4 x+ 3 x+− 2 x+−x= ...

Basic algebra 63 = 5 × 2 × ( 2 5 ) 2 × ( 5 2 ) 3 since 2 1 2 = 5 2 = 5 1 × 2 1 × 2 5 × 2 5 × 5 2 × 5 2 × 5 2 = 1 1 × 1 1 × 1 1 × ...

64 Basic Engineering Mathematics (i) (iv) (vii) x^2 −xy+y^2 x+y ) x^3 + 0 + 0 +y^3 x^3 +x^2 y −x^2 y +y^3 −x^2 y−xy^2 xy^2 +y^3 ...

Basic algebra 65 (2) am an =am−n For example, c^5 c^2 =c^5 −^2 =c^3 (3) (am)n=amn For example, ( d^2 ) 3 =d^2 ×^3 =d^6 (4) a m n ...

66 Basic Engineering Mathematics Using law (3) of indices gives d^2 e^2 f^1 /^2 (d^3 /^2 ef^5 /^2 )^2 = d^2 e^2 f^1 /^2 d^3 e^2 ...

Basic algebra 67 The HCF of each of the three terms isa^1 /^2 b. Dividing each term bya^1 /^2 bgives a^2 b ab^2 −a^1 /^2 b^3 = a ...