Page 90 - Start Up Mathematics_7

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
5
3
2
7
1
(a) (–3) × (–3) × (–3) (b) (6 × 6 × 6 ) ÷ 6 5
5
2 3
2 3
–3 2
(c) (3 ) ÷ 3 (d) {(–5) } × {(–5) }
5. State true or false and justify your answer:
2
3
3
0
0
3
3
3
3
(a) 3 × 5 = 15 (b) 2 > 3 (c) 5 × 6 = 30 (d) 3 × 2 = 5 0
6. Simplify each of the following:
2
3
8
3
2
3
49 × 7 × 100 121 × 5 3 a × b × b × a 2 2 × 4 × 5 3
(a) (b) (c) (d)
2
3
3
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  4  () 3  6 – 1 7 9 – 3 5 5
5
6
(a)   (b)   (c) ( c m 2 (d) ( c m 2
 7   9  3 5
8. Simplify and answer each of the following in exponential form:
– 3 5 – 3 4 – 3 8 1
2 3
(a) c m × c m ÷ c m (b) {(–3) } ×
3 2
31 31 31 {(–3) }
3
19
17
(c) (5 × 5 ) ÷ 5 37 (d) ( c – 2 m 7 ÷ c – 2 m 2 × c – 2 m 2
5 5 5
9. Simplify each of the following and express each as a rational number:
2 4 3 2 2 3 3 4 7 3
(a) × (b) × ×
3 4 3 5 2
– 1 5 3 2 – 3 3 – 5 3
3
(c) c 3 m × 3 × 4 (d) c ( 4 m ÷ c 2 m 2 ÷ 2 3
8
7
10
11
10. Simplify c ( 3 m × c 3 m 2 ÷ c ( 3 m × c 3 m 2 and express the result as power of 10.
17 17 17 17
11. Determine the value of x in each of the following:
3 7
9
7x
11
(a) {(3) } = 3 (b) (–2) ÷ (–2) = (–2) 2x
21
x
(c) (47) ÷ (47) = (47) 45 (d) 2 ÷ 2 = 2 3
3 3 3
12. Simplify:
  −   −2  −1 – 9 – 2 3 2 - 1 – 5 - 1 - 1
2

1
(
–1
–1 –1
(a)         (b) c 2 m ÷ c m (c) c m ÷ c m 2 (d) (3 – 5 )
     3      3 3 3 2
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