Task 2.8.1. Observe the pattern
1. Observe the pattern and fill in the blanks
5 = 1 × 5
5 + 5 = 2 × 5
5 + 5 + 5 = 3 × 5
5 + 5 + 5 + 5 =.........
5 + 5 + 5 + 5 + 5 =......
5 + 5 + 5 + 5 + 5 + 5 =......
This observation is to write the tables.
2. Observe the pattern and fill in the blanks
5 = 5¹
5 × 5 = 5²
5 × 5 × 5 = ......
5 × 5 × 5 × 5 = ......
5 × 5 × 5 × 5 × 5 = ......
5 × 5 × 5 × 5 × 5 × 5 = ......
5 × 5 × 5 × 5 × 5 × 5 × 5 = ......
This observation is used to write the exponential form.
3. Observe the pattern and fill in the blanks
a = a¹
a × a = a²
a × a × a = a³
a × a × a × a = a⁴
a × a × a × a × a = a⁵
a × a × a × a × a × a = a⁶
a × a × a × a × a × a × a = a⁷
The result of these observations is written with two numbers Big and Small numbers as (a²). Big number is called Base and Small number is called exponent or power.
a² –> read as 'a squared' or 'a raised to the power 2'
a³ –> read as 'a cubed' or 'a raised to the power 3'
a⁴ –> read as a raised to the power 4 or the 4th power of a)
a⁷ –> read as a raised to the power 7 or the 7th power of a
a³ × b² –> read as a cubed b squared
2. Express the following in exponential form:
(i) 6 × 6 × 6 × 6
(ii) t × t
(ii) b × b × b × b
(iv) 5 × 5 × 7 × 7 × 7
(v) 2 × 2 × a × a
(vi) a × a × a × c × c × c × c × d
1. Find the value of:
(i) 2⁶
(ii) 9³
(ii) 11²
(iv) 5⁴
(1)⁵, (-1)³, (-1)⁴, (-10)³, (-5)⁴
Express:
(ii) 128 as a power of 2
(iii) 256 as a power 2
(iii) 512 as a power 2
(i) 729 as a power of 3
(ii) 625 as a power of 5
(iii) 343 as a power of 7
Express each of the following numbers using exponential notation:
(i) 512
(ii) 343
(iii) 729
(iv) 3125
5 Express the following numbers as a product of powers of prime factors:
(i) 72
(ii) 432
(ⅲ) 1000
(iv) 16000
4. Identify the greater number, wherever possible, in each of the following?
(1) 4 or 3⁴
(ii) 5³ or 3⁵
(iii) 2⁸ or 8²
(iv) 100² or 2¹⁰⁰
(v) 2¹⁰ or 10²
5. Express each of the following as product of powers of their prime factors:
(i) 648
(ii) 405
(iii) 540
(iv) 3,600
6. Simplify:
(1) 2 × 10 ³
(ii) 7² * 2²
(ii) 2³ * 5
(iv) 3 * 4⁴
(v) 0 * 10⁴
(vi) 5² * 3³
(vii) 2⁴ * 3²
(viii) 3² * 10⁴
7. Simplify:
(1) (- 4)³
(ii) (–3) * (– 2)³
(iii) (–3)² * (–5)²
(iv) (–2)³ * (–10)³
8. Compare the following numbers:
(i) 2.7 * 10¹²; 1.5 * 10⁸
(ii) 4 * 10¹⁴; 3 * 10¹⁷
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