Page 41 - WCS - Electrical

28+
+
4
56
−
4

-
9
+
− 96
28+ + + - 72 = = = = + −8 7 14
+16
=
7
4 28
+ + − 6 20 7
5y
56 =
+
+
=
WORKSHOP CALCULATION & SCIENCE - CITS
4 28
14
+ +
−
=
5
5 7
=
+
x 4
+
- - + - + 4 56 = = −8 − 14
72
4 56
+ - 4 9 72 = − 14
4
-
5x =
− 96
Division = = 25 −8
9 72
+ -
+16
5
− 6 96 = 5−8
−
10a 9
1 5y − − + = 6 96 20+= 16
2a
=
5 5y 5 20 +16
8ac = 6
−
x − 5 5y 5 20
2bc =
-3ax ÷ -6x
2 4x 5m −×5 6n − 7p
−5
5x = 25
4 x
28mn
5 5x − 20
5 25
4
5a + =
15xy ÷ -5
3 10a 5 25
5 5x
7a + =
2a m 5 28 5
10a
a 8ac
10a
− 2a = a m− n
8a
4 n 2bcc
− − a 2a 6n − 7p
5m −×
3
8ac
2 2bc 2 − 6n −− 2 = 7p 1 2
3
−
2 =
−
− ×
=28mn
5m
22bc
5 5a + 20 28mn 7p6n −−×
2
−
5m
−
2×
2×
7a ++ 28 20 2 = 8 = 2
5a
−
28mn
m
2×
28 20
a 5a + 2 m− n 4
7a +
6 n = a a  n
m

= 28
a a n a 7a + =  m−
 n
a
n 3 m
b 
b 2 n = =  3 m− n 2 = 2
a
1
a
a
2 −
2 2 =
3 3 n
2×
2
4
2 

2 2 2 a
3
1
2
Algebra - Theory of indices, Algebraic formula, related
= =
= 2
= 2 ==
 2
 2 −
3
2
8
2 2×
2×
2 2
9
3
3× 1
 3
3 2
2
=

3  =
2
=
2 =
2 =
2 −
n 2×
1 48
2 2
2×
− 2× 2
problems 2 2
2
n =
=
=
a n
4 8
n  2
×
a 2× 22×
a 2
a
=

 =
=
n
1
n
n a 2×
2 b  a  42
− 
2 b
=
=
Calculations involving powers

 n
n
2 2  
2 b 3 n a =     b a 2 2   2× 2 4
2 

=
Power : Concept 2 32 = 94
=
2

7 

3  b 
 3 n
2 2 b
3× 2×
1   2 
3 
a.a.a... upto n times is = a
 3  n 2 3 =   =    2  = 3 2 = 9 4 n

−2
4  2×
4  1 2 
a3 =  3   3× =
49 =
7 
=
7
× n 2
n 1
9
3
3×
= a 3 
a 3 − a is the base, n is the exponent.

=
16
4
4 1 n 1
2
−
n
−
2
= a
=
a
When a number, say 2 is multiplied by itself 4 times, we write it as 24 (two to the power of 4) and it is equal to
2 1 n
2
2 − 2 = a
2
2
2 1
2 x 2 x 2 x 2 = 16.
 −
7 
3  2
 2
2
=

=

1  2
 2
2

4  7 
4  3  2

The exponent denotes how many times the base number is multiplied by itself.
7   1  2 =   4   2
49
7
4 3 
7 

= 

×
Powers with a positive base have a positive result.
=

1 


16 49
47
47
4 


4 
=
×
4 7
4 7
Powers with a negative base and with an exponent that is even will have a positive result.
16 49
×
=
4
The sign 4 16
(+a) = a n
n
(– a) = a 2n
2n
(2) = 2 x 2 = 4 and
2
(– 2) = – 2 x – 2 = +4 but
2
(– 2) = – 2 x – 2 x – 2 = – 8
3
Addition and subtraction of powers
Powers with the same base and exponents can be added or subtracted by addition or subtraction of the coefficients.
x.a + y.a n = a (x + y)
n
n
x.a – y.a = a (x – y)
n
n
n
Ex .4x + x – 3x = x (4 + 1 – 3) = 2x .
2
2
2
2
2
Multiplication
Powers with the same bases are multiplied by involving the common base raised to the power of sum of the
exponents.
28
CITS : WCS - Electrical - Exercise 4