Page 74 - ICSE Math 7

3 2
2
16a (b )
=
2 3
2 3
512(a ) (b )
2 6
16a b
m n
= [Using (a ) = a m×n ]
6 6
512a b
1  a m 1 
= Using =
−
32a 6–2   a n a n m 

1
=
32a 4
−
4
 1 − 3  3  1
0
2 0
–4
–6
(c) (3 ) + 3 ÷ 3 +   = 3 + +
6 
 3  3  3 − 3

−
= 1 + (3 –4–(–6) ) + 3 3
 0 a m mn 1 m 
−
 Using a = 1, n = a and − m = a 
 a a 
= 1 + (3 –4+6 ) + 27
2
= 1 + 3 + 27
= 1 + 9 + 27 = 37
  5  2 4    − 3  2 125   25 4   9 125 
÷
(d)    ×  ÷    ×  =  64 ×   25 × 

   8  5     5  81   5   81 

 5   5 5 9 9
=   ÷   = × =
 16  9 16 5 16
EXERCISE 5.2
–3
1. By what number should 2 be multiplied so that the product is 16?
–1
–1
2. By what number should (3) be multiplied so that the product is (6) ?
–1
–1
3. By what number should (–9) be divided so that the quotient is (18) ?
4. Using the laws of exponents, simplify and write the answer in exponential form.
11
7
3
5
1
2
(a) (–3) × (–3) × (–3) (b) (6 × 6 × 6 ) ÷ 6 5
2 3
–3 2
2 3
5
(c) (3 ) ÷ 3 (d) {(–5) } × {(–5) }
5. State true or false and justify your answer:
0
3
3
0
3
3
3
3
2
(a) 3 × 5 = 15 (b) 2 > 3 (c) 5 × 6 = 30 (d) 3 × 2 = 5 0
6. Simplify each of the following:
3
2
9
3
2
49 × 7 × 100 121 × 5 3 a × b × b × a 2 2 × 4 × 5 3
3
(a) (b) (c) (d)
3
3
2
10 × 3 × 7 2 11 × 5 a × b 16 × 10 2
2
7. Using laws of exponents, compute each of the following and answer in exponential form.
3

   6   4    5   6 – 1 7 9 – 3 5 5
3

(a)     (b)     (c) ( c 3 m 2 (d) ( c m 2

   7      9   5

60