Page 92 - Mathematics_Form_Two

Exponents and radicals

(i) 3 13= × read as the “third power of 2” or “2 raised

(ii) 4 22= × to exponent 3”.
Engage in Activity 5.2 to explore more
(iii) 8 222= ×× about exponential numbers.

(iv) 12 = 2 2 3××
(v) 81 3333= ××× Activity 5�2: Identifying features of
FOR ONLINE READING ONLY
Mathematics for Secondary Schools From the given examples, the same 1. Choose any counting number greater

powers, base, and
These are expanded form of numbers.

exponent of the numbers

numbers that are multiplied several times
than 1 and multiply it several times.
can be expressed in short form. Some
numbers can be expressed in short form
2. Write the product in the power form
by counting the number of times the same
and identify the power, base, and
exponent.
number is multiplied and writing the result
on the top right hand of the multiplied 3. Share your work and justify your
number. For example: answers.
(i) 42 22= ×= 2 since 2 is multiplied
repeatedly two times. Generally, a is a number written in
n
(ii) 8 222 2= ×× = 3 since 2 is exponential form, where a is the base and
multiplied repeatedly three times.
n
n is the exponent. The number a is called
(iii) 12 = 2 2 3 2×× = 2 × 3 since 2 is a power.
multiplied repeatedly two times,
and three is multiplied once.
Example 5�1
(iv) 81 3333 3= ××× = 4 since 3 is
multiplied repeatedly four times. Write each of the following expressions
in exponential form:

3
2
Numbers expressed in the forms 2 , 2 (a) 5 × 5 × 5 × 5
4
and 3 are called powers. The numbers (b) k × k × k × k × k
which are multiplied several times are (c) (–3) × (–3) × (–3) × (–3) × (–3)
called bases, and the number of times any
number is multiplied by itself is called (d) m × m × m × ... × m (n times)
5
exponent. For example, 3 : Solution
5
3 is the power, where
(a) 5 × 5 × 5 × 5 = 5
4
3 is the base and
(b) k × k × k × k × k = k 5
5 is the exponent.
(c) (–3) × (–3) × (–3) × (–3) × (–3) =
(–3) 5
Likewise, 3 is read as the “fifth power of n
5
3
3” or “3 raised to exponent five” and 2 is (d) m × m × m × ... × m = m
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Student's Book Form Two

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MATHEMATIC F2 v5.indd 86
MATHEMATIC F2 v5.indd 86 11/10/2024 20:12:11