Page 38 - ICSE Math 8

7 
9. By what number should    − 1 be divided to give the quotient as 25 ?
 3  21

7
–4
–3
2m
5
2
10. Find the value of m, if: (a) (6) ÷ (6) = (6) (b) (9) –3m ÷ (9) = (9) (c) (–5) m – 1 ÷ (–5) = (–5) –6
AT A GLANCE
¾ If x is a non-zero rational number and n is any positive integer, then
1
–n
0
n
(a) (x) = x × x × x × x × ... n times (b) (x) = (c) (x) = 1
x () n
¾ Laws of exponents: If x and y are two non-zero rational numbers and m and n are any two integers, then
x () m
m
m
n
n
m n
(a) (x) × (x) = (x) m + n (b) = (x) ÷ (x) = (x) m – n (c) (x ) = (x) mn
x () n
 x  n x () n
(d)   = (e) (x) × (y) = (xy) n
n
n
y
  y () n − n n n
p  p   q  q ()
¾ If is any non-zero rational number and n is a positive integer, then   =   = .
q  q   p  p () n
MENTAL MATHS
1. Choose the correct option.
2
(
–5
(a) The value of (2) × 64 3 ) is:
1 1
(i) 512 (ii) 512 (iii) 16 (iv)

−3
   −   2 2
2
(b)     is equal to:
   3   
(i) 3 (ii) 64 (iii) 81 (iv) 729
2 729 32 64
− 
(c) Which of the following is not equal to  2  4 ?

 5 
2 4  2 −   2 −  − ( ) 2 4 () 2 4
−   2
−   2
(i) (ii)         (iii) (iv) −
×
×
×
− ( 5) 4  5   5   5   5  () 5 4 () 5 4
 2 −6  2 4
− 
− 
(d)   ÷   is equal to:
 7   7 
− 
− 
− 
− 
(i)  2  2 (ii)  2  −10 (iii)  7  −10 (iv)  7  2




 7   7   2   2 
–1
–1
–1
(e) {(4) – (2) } × (3) is equal to:
(i) −1 (ii) 1 (iii) 3 (iv) −3
12 12 8 8
2. Write True or False.
7 –2 15 2
0
(a) x = 0. (b) = .
15 7
(c) If {(2) 3m – 1 + 10} ÷ 7 = 6, then m is 2.
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