## Chapter 13 Exponents and Powers Exercise 13.1

Question 1: Find the value of:
(a) 2⁶

= 2 x 2 x 2 x 2 x 2 x 2
= 64

(b) 9³

= 9 x 9 x 9
= 729

(c) 11²

= 11 x 11
= 121

(d) 5⁴

= 5 x 5 x 5 x 5
= 625

Question 2: Express the following in exponential form:
(a) 6 x 6 x 6 x 6
= 6⁴

(b) t x t
= t²

(c) b x b x b x b
= b⁴

(d) 5 x 5 x 7 x 7 x 7
= 5² x 7³

(e) 2 x 2 x a x a
= 2² x a²

(f) a x a x a x c x c x c x c x d
= a³ x c⁴ x d¹

Question 3: Express each of the following numbers using exponential notation:
(a) 512

(ii) 343

(iii) 729
(iv) 3125

Question 4: Identify the greater number, wherever possible, in each of the following?
(i) 4³ or 3⁴
4³ = 4 x 4 x 4
= 64
3⁴ = 3 x 3 x 3 x 3
=
81
64 < 81
Therefore,
3⁴ is greater.

(ii) 5³ or 3⁵
5³ = 5 x 5 x 5
= 125
3⁵ = 3 x 3 x 3 x 3 x 3
= 243
125 < 243
Therefore,
3⁵ is greater.

(iii) 2⁸ or 8²
2 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
8² = 8 x 8
= 64
256 < 64
Therefore,
2 is greater.

(iv) 100² or 2¹⁰⁰
100² = 100 x 100
= 10000
2
¹⁰  = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 1024¹⁰
10000 < 1024¹⁰
Therefore,
2
¹⁰⁰ is greater.

(v) 2
¹⁰ or 10²
2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 1024
10²
= 10 x 10
= 100
1024 < 100
Therefore, 2
¹⁰ is greater.

Question 5: Express each of the following as product of powers of their prime factors:
(i) 648

(ii) 405

(iii) 540

(iv) 3,600

Question 6: Simplify:
(i) 2 × 10³
= 2 × 10 × 10 × 10
= 2 × 1000
= 2000

(ii) 7² × 2
²
= 7 × 7 × 2 × 2
= 49 × 4
= 196

(iii) 2³ × 5
= 2 × 2 × 2 × 5
= 8 × 5
= 40

(iv) 3 × 4⁴
= 3 × 4 × 4 × 4 × 4
= 3 × 256
= 768

(v) 0 × 10²
= 0 × 10 × 10
= 0 × 100
= 0

(vi) 5² × 3³
= 5 × 5 × 3 × 3 × 3
= 25 × 27
= 675

(vii) 2⁴ × 3²
= 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9
= 144

(viii) 3² × 10⁴
= 3 × 3 × 10 × 10 × 10 × 10
= 9 × 10000
= 90000

Question 7: Simplify:
(i) (-4)³
= -4 × -4 × -4
= -64

(ii) (-3) × (-2)³
= -3 × -2 × -2 × -2
= -3 × -8
= 24

(iii) (-3)² × (-5)²
= -3 × -3 × -5 × -5
= 9 × 25
= 225

(iv) (-2)³ × (-10)³
= -2 × -2 × -2 × -10 × -10 × -10
= -8 × -1000
= 8000

Question 8: Compare the following numbers:
(i) 2.7 × 10¹² ; 1.5 × 10⁸
2.7 × 10¹² ____ 1.5 × 10⁸
Comparing the exponents of base 10.
2.7 × 10¹² > 1.5 × 10⁸

(ii) 4 × 10¹⁴ ; 3 × 10¹⁷