## Selina Concise Mathematics class 7 ICSE Solutions – Exponents (Including Laws of Exponents)

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**EXERCISE 5 (A)**

**Question 1.**

**Find the value of:**

** (i) 6² **

** (ii) 7 ^{3}**

**(iii) 4**

^{4}**(iv) 5**

^{5}**(v) 8**

^{3}**(vi) 7**

^{5}**Solution:**

**(i)** 6^{2} = 6 x 6 = 36

**(ii)** 7^{3} = 7 x 7 x 7 = 343

**(iii)** 4^{4} = 4 x 4 x 4 x 4 = 256

**(iv)** 5^{5}= 5 x 5 x 5 x 5 x 5 = 3125

**(v)** 8^{3} = 8 x 8 x 8 = 512

**(vi)** 7^{5 }= 7 x 7 x 7 x 7 x 7 =16807

**Question 2.**

**Evaluate:**

** (i) 2 ^{3} x 4^{2}**

**(ii) 2**

^{3}x 5^{2}**(iii) 3**

^{3}x 5^{2}**(iv) 2**

^{2}x 3^{3}**(v) 3**

^{2}x 5^{2}**(vi) 5**

^{3}x 2^{4}**(vii) 3**

^{2 }x 4^{2}**(ix) (5 x 4)**

^{2}**Solution:**

**(i)** 2^{3} x 4^{2}

= 2 x 2 x 2 x 4 x 4

= 8 x 16

= 128

**(ii)** 2^{3} x 5^{2}

= 2 x 2 x 2 x 5 x 5

= 8 x 25

= 200

**(iii)** 3^{3} x 5^{2}

=3 x 3 x 3 x 5 x 5

= 27 x 25

= 675

**(iv)** 2^{2} x 3^{3}

= 2 x 2 x 3 x 3 x 3

= 4 x 27

= 108

**(v)** 3^{2} x 5^{3}

=3 x3 x 5 x 5 x 5

= 9 x 125

= 1125

**(vi)** 5^{3} x 2^{4}

= 5 x 5 x 5 x 2 x 2 x 2 x 2

= 125 x 16

= 2000

**(vii)** 3^{2} x 4^{2}

=3 x 3 x 4 x 4

= 9 x 16

=144

**(viii)** (4 x 3)^{3}

=4 x 4 x 4 x 3 x 3 x 3

= 64 x 27

= 1728

**(ix)** (5 x 4)^{2}

=5 x 5 x 4 x 4

= 25 x 16

= 400

**Question 3.**

**Evaluate:**

**Solution:**

**Question 4.**

**Evaluate :**

**Solution:**

**Question 5.**

**Which is greater :**

** (i) 2 ^{3} or 3^{2}**

(ii) 2^{5} or 5^{2}

**(iii) 4**

(iv) 5

^{3}or 3^{4}(iv) 5

^{4}or 4^{5}**Solution:**

**(i)** 2^{3} or 3^{3}

Since, 2^{3} = 2 x 2 x 2 = 8

and, 3^{2} = 3 x 3 = 9

∵9 is greater than 8 ⇒ 3^{2} > 2^{3}

**(ii)** 2^{5} or 5^{2}

Since, 2^{5} = 2 x 2 x 2 x 2 x 2 = 32

and, 5^{2} = 5 x 5 = 25

∵32 is greater than 25 ⇒ 2^{35} > 5^{32}

**(iii)** 4^{3} or 3^{4}

Since, 4^{3} = 4 x 4 x 4 = 64

and, 3^{4} = 3 x 3 x 3 x 3 = 81

∵ 81 is greater than 64 ⇒ 3^{4} > 4^{3}

**(iv)** 5^{4} or 4^{5}

Since, 5^{4} = 5 x 5 x 5 x 5 = 625

and, 4^{5 }= 4 x 4 x 4 x 4 x 4= 1024

∵ 1024 is greater than 625 ⇒ 4^{5} > 5^{4}

**Question 6.**

**Express each of the following in exponential form :**

** (i) 512**

** (ii) 1250**

** (iii) 1458**

** (iv) 3600**

** (v) 1350**

** (vi) 1176**

**Solution:**

**(i)** 512

**(ii)** 1250

**(iii)** 1458

**(iv)** 3600

**(v)** 1350

**(vi)** 1176

**Question 7.**

**If a = 2 and b = 3, find the value of:**

** (i) (a + b) ^{2}**

**(ii) (b – a)**

^{3}**(iii) (a x b)a (iv) (a x b)b**

**Solution:**

**(i)** (a + b)^{2}

= (2 + 3)^{2} = (5)^{2} = 5 x 5 = 25

**(ii)** (b – a)^{2}

= (3 – 2)^{2}= (1)^{3}

= 1 x 1 x 1 = 1

**(iii)** (a x b)^{a}

= (2 x 3)^{2} – (6)^{2}

= 6 x 6 = 36

**(iv)** (a x b)^{b}

= (2 x 3)^{3} = (6)^{3} = 6 x 6 x 6 = 216

**Question 8.**

**Express:**

** (i) 1024 as a power of 2.**

** (ii) 343 as a power of 7.**

** (iii) 729 as a power of 3.**

**Solution:**

**(i)** 1024 as a power of 2.

**(ii)** 343 as a power of 7.

**(iii)** 729 as a power of 3.

**Question 9.**

**If 27 x 32 = 3 ^{x} x 2^{y}; find the values of x and y.**

**Solution:**

**Question 10.**

**If 64 x 625 = 2 ^{a} x 5^{b}; find :**

**(i) the values of a and b.**

**(ii) 2**

^{b}x 5^{a}**Solution:**

**(i)** the values of a and b.

**(ii)** 2^{b} x 5^{a}

**EXERCISE 5 (B)**

**Question 1.**

**Fill in the blanks:**

** In 5 ^{2} = 25, base = ……… and index = ……….**

**If index = 3x and base = 2y, the number = ………**

**Solution:**

**(i)** In 5^{2} = 25, base = 5 and index = 2

**(ii)** If index = 3x and base = 2y, the number = 2y^{3x}

**Question 2.**

**Evaluate:**

** (i) 2 ^{8} ÷ 2^{3}**

**(ii) 2**

^{3÷}2^{8}**(iii) (2**

^{6})^{0}**(iv) (3**

^{o})^{6}**(v) 8**

^{3}x 8^{-5}x 8^{4}**(vi) 5**

^{4 }x 5^{3}+ 5^{5}**(vii) 5**

^{4}÷ 5^{3}x 5^{5}**(viii) 4**

^{4}÷ 4^{3}x 4^{0}**(ix) (3**

^{5}x 4^{7}x 5^{8})^{0}**Solution:**

**Question 3.**

**Simplify, giving Solutions with positive index:**

**Solution:**

**Question 4.**

**Simplify and express the Solution in the positive exponent form :**

**Solution:**

**Question 5.**

**Evaluate**

**Solution:**

**Question 6.**

**If m ^{2} = -2 and n = 2; find the values of:**

**(i) m + r**

^{2}– 2mn**(ii) m**

^{n}+ n^{m}**(iii) 6m**

^{-3}+ 4n^{2}**(iv) 2n**

^{3}– 3m**Solution:**