Page 70 - ICSE Math 7

• A negative rational number raised to an odd power is always negative.
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9
For example, (–1) = –1 (–1) = –1
p  p  n p n 2 5 2 5
• If is any rational number and n any integer, then = . For example, =
q  q  q n 3 3 5


EXERCISE 5.1

4
5
5
1. Find the value of: (a) 2 (b) 3 (c) 7 (d) 11 4
2. Write the following in exponential form.
(a) 7 × 7 × 7 × 7 × 7 (b) 2 × 2 × 3 × 3 × 3 × 3 (c) x × x × x × y × y × z × z
3. Express each of the following numbers using exponential notation.
(a) 12,500 (b) 27,000 (c) –343 (d) 62,500

4. Compare the following.
4
3
4
3
3
5
6
(a) 3 and 4 (b) (–2) and 1 (c) 3 and 5 (d) 2 and 6 2
5. Evaluate the value of each of the first five natural numbers raised to the power 4.
6. To what power should (–2) be raised to get 64?
7. Simplify.
2
5
4
5
11
3
(a) (–5) × 2 (b) (–1) × (–2) × (–3) (c) (–3) × (–5) 3
8. Express each of the following in the powers of their prime factors.
(a) 288 (b) 1,250 (c) 24,200 (d) 2,048
9. Express the following in exponential notation.
3 × 3 × 3 × 3 × 3 (–3) × (–3) × (–3) × (–3) × (–3) × (–3) × (–3)
(a) (b)
5 × 5 × 5 × 5 × 5 5 × 5 × 5 × 5 × 5 × 5 × 5
(–5) × (–5) × (–5) × (–5) × (–5) × (–5) 11 × 11 × 11 × 11 × 11 × 11
(c) 9 × 9 × 9 × 9 × 9 × 9 (d) 22 × 22 × 22 × 22 × 22 × 22
10. Express the following rational numbers in exponential notations. Further, express them as power
of prime factors.
27 512 –625 –1
(a) (b) (c) (d)
1,000 729 1,296 125
Laws of Exponents

m
n
Law 1: a × a = a m + n , where a is non-zero rational number and m, n are whole numbers.
5
2
7
We know 3 × 3 = (3 × 3 × 3 × 3 × 3) × (3 × 3) = 3 . We can get the same result by adding their
5
7
2
powers, i.e., 3 × 3 = 3 5 + 2 = 3 .
Similarly, Try This
 4  5  4  2  4 4 4 4 4   4 4   4  7 Find the value of the following.
×
  ×   =  × × × ×   ×  =   4 5
 5   5   5 5 5 5 5   5 5   5  (a) 7 × 7 (b) 3 × 3
2
5
4 4
 4  5  4  2  4  52+  4  7 (c) 2 7 × 2 9
which is the same as   ×   =   =   . 5 5
 5   5   5   5 
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