Page 68 - ICSE Math 7

5 Exponents and Powers

Key Concepts

• Exponents • Scientific Notation of Numbers
• Laws of Exponents • Application of Laws of Exponents

Do you know that the approximate distance between the sun and
the earth is 150,000,000,000 m and the approximate distance
between the sun and Saturn is 1,426,000,000,000 m. Can you
tell which of the two planets earth or Saturn is nearer to the
sun? Did you find it difficult to read these large numbers?
To make it convenient to read and understand large numbers
we use exponents.
Exponents help us to read, understand and compare very large
and very small numbers like population of countries, distance
between planets and size of atoms.

Exponents
7
Large number like 10,000,000 can be written in shorter form as 10 . Clearly, 10,000,000 =
7
10 × 10 × 10 × 10 × 10 × 10 × 10 = 10 . It is read as 10 raised to the power 7 or seventh power of
7
7
10. 10 is called the exponential form of 10,000,000. In 10 , base is 10 and exponent is 7.
8
Also, 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2 , here base is 2 and exponent is 8. Some powers have
2
special names. For example, 5 , which is 5 raised to the power 2, also read as ‘5 squared’ means 5 is
3
to be multiplied by itself two times and 5 , which is 5 raised to the power 3, also read as ‘5 cubed’
means 5 is to be multiplied by itself three times.
In general, for any rational number a and a whole number n, we define
n
a = a × a × a × … × a (n times)
n
th
a is called the n power of a and is also read as a raised to the power n.
The rational number ‘a’ is called the base and n is called the exponent or power or index.
3
7
3
Example 1: Find the value of: (a) 2 (b) 7 (c) 11 (d) –5 3
8
3
7
Solution: (a) 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128 (b) 7 = 7 × 7 × 7 = 343
3
(c) 11 = 11 × 11 × 11 = 1,331 (d) –5 3 = –5 × –5 × –5 = –125
8 8 8 8 512
Example 2: Express the following in exponential form.
(a) 2 × 2 × 2 × 2 (b) x × x × x × x × x
(c) 3 × 3 × 3 × 3 × b × b × b (d) a × a × c × c × c × d × d

Solution: (a) 2 × 2 × 2 × 2 = 2 4 (b) x × x × x × x × x = x 5
2 3 2
4 3
(c) 3 × 3 × 3 × 3 × b × b × b = 3 b (d) a × a × c × c × c × d × d = a c d
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