Page 42 - WCS - Electrical

28+
28+
+
28+ + 4 = = + 7 7
=
4
+ 56 + 7 WORKSHOP CALCULATION & SCIENCE - CITS
+
+ 4
+
14
+ + 56 = = − − 14
56 28
- 28
+
4 = +=
14 7
−
-
72 44
--+ 4 = + 7
72 4
−8
- + m −= 8
=
- +
72 56
+ 56
n
−8 14
9 = =
−
9
+ + a x a = a m + n .
=
14
−
+
− 96 94-
− 96 4-
2 +16
3 =
− 96 72- - 2 x 2 = 2 + 2 = 2 5
+16
3
=
72
− 6 = −= 8
+16
− 6 =
20
5y − 69
+
(2 x 2 x 2) x (2 x 2) = 2 x 2 x 2 x 2 x 2 = 25
= 20
5y 9 = 20 −8
+
5y − 96
− 96
5 = =
5 +16
5
=
5 +16
8 x 4 = 32.
5
x 5− 6
x − 6
x5y
20
= 20
4 5y
4
Powers with the same exponent of different base numbers are multiplied by involving the product of the base
=
4
25 5
5x 5
5x 5
= 25 5
numbers raised to the common exponent.
5x x
= 25
5
x
5 =
5
5
10a
5 4
a x b = (a x b)
n
10a
4
10a n 5 25 n
5x
2a = 255x
2a =
2 x 3 = (2 x 3) 2
2
2
2a 5
8ac 5
− 8ac 55
− 8ac
10a
− 10a
2bc
2 x 2 x 3 x 3 = 6 x 6 = 36
2bc
5m −×
6n −
7p
2a
−2bc
6n −
5m −×
− 2a
6n −
− 8ac
5m −×
7p

Division 28mn 7p
−c
− 8a 28+
− 28
− +
28mn
20 28mn 7
5a + − 2bc +=
7
=
+
20
5a + 2bc
5a + 5m 4
− +
Powers with like bases are divided by involving the base raised to the difference between the exponents.
20 6n −−×
7p
4
+
28 6n −−×
7a + 5m
+
− 56
7a + 56 − 14 7p
+
28
7a + − =
m 28 28mn
=
−
am −
28mn
n
am 5a + 4- - 4 = 20 m− 14
n
am−
n = 20a +
a5 72-
n
am−
a
an =
28 −= 8
7a + =
an - 72 28 −8
3 7a +
23 m 9
a +
9
+
3
am
23 − 96 = 2 − nm− 2 = 1 1 2 2
2 =
2 a− 96
= 3
a
2 = 3 += 16
2 − nm−
2 = 1
2 =
22 = n = += 16
a
an − 6
22− 6 2 − 2 = 2 = 2
2 a
8
2
2×
20
2× 3 5y
5y
= 8
220
=
2 3
2 1
2× 23 =
= 8
2×
2× 2 2× 2 = 55 2× 2 = − 4 2 = = 1 = 2
=
2
2 2 =
2× 2 −= 3
2 25
2
5
4 = 22 =
n 2
2×
22 x
an 2 x
  n 8
an 2× = a22   × a  n n4
= a ×
2
  = 8
a2×
  2
=
2
4
n 4
Powers with the same exponents are divided by involving the quotient of the bases by the common exponent.
2
=
=
b   =
 
bn 2× 255x
5x
2
bn 2×  2 b  25 4 4
b 
3  =
b n =  a 5 2 n 2× 2 4

23 an 5
2 2  n
= 2×
23 a5 = 2    2  5   = 2× 2 = 4
  = a
= 4
= 2 

2
2 10a

  =
2 n 10a
3×
9
=
3  =
  b 
32 bn
3×
3
9
3
32 b 2a   3  b  3× 3 3 = 9
1  2

3
−3
n 2a
= 1 2 2
2
2×
− 23
a n8ac
a n = 22 8ac   an  = = 2× 2 = 4 4
= 1 
n  
− −
a −
=
= 
=
9
3×
3
2 2bc

322bc
a 
1 3 
− 3 −
2 5m −×
7p
2 2 n 5m an 3  6n − 3× 3 9
7p
= 1 16n −−×
− − −
= 1
2 2 = 2 1
− a n
−
2 a
= = 28mn
−
22 n
Only like powers can be added or subtracted.
22 28mn
−
2 an
2
5a +
2 20
 5
3  2 a 20a +
Examples   2 =28     1   7  2
= 7
1   −
3 2
  2
1   = 1
  2 2
3 −
= 7
 
7a +
28
27a +
4  = 2

4  
1  m
 22
4 

4 
7 4 a m
 2
n
 a
7  2 m−
(The exponent 1 is usually not written.)
49 4  2
n
× 7 2 a m−
7
= 49
=
7 
= 49 
7  2
× 7  a
3 =
= 7
4 ×   n
16  
1 4 =  
a
1 3 n
4 1  a 4  16    4   
=
a = a164
4
4
4 3
4 
2 3
1
 3
7 2 3
1
49 2 =−
2 =
2
2 =2=× 7 2
7 7 2 × 2 1 = = 49 2 =− 2 = 2
=
4 2 2
4
16
2
4 2× 2 4 22× 2 16 2 8 2 2
8
2×
2×
2a + 3a = 5a
=
=
2× 2 = 4 = 2
4
2
2×
(Any number raised to the power of 0 is 1.)
n
a n n 0 =    a   n
a
a 
a = 1
b 

b n n =   b  
b
0 3
2
2 3 =    2  2 = 2× 2 = 4
2 = 1 2 
2
2
2×
4

=
=
=


2
9
3
3×
3 2
A number raised to a negative power corresponds to its reciprocal with the exponent’s sign changed to +.
3 
3
3×
9
 3 

3
1
−
n
a n = 1 n
−
a
=
a n
a
1
2
−
2 2 = 1
−
=
2
2
2 2
2 2 2
2
2

7 
Powers are involved by multiplying the exponents.

3 
3 

7 

=
1 



=



1 
4
m n 4
n m 
(a ) = (a ) 

  4   4 
7 2 × 7 3 = 49
7
7
49
(2 ) = 2 = 2
2.3
4 × 4 = 16 6
16
4
4
Powers can be transposed without affecting the result.
(a ) = (a )
n m
m n
(2 ) 3 = (2 ) 2
3
2
29
CITS : WCS - Electrical - Exercise 4