Table of Contents

Toggle## Class 7, Maths, Chapter 13, Exercise 13.1 Solutions

**Q.1. Find the value of:**

**(i) 2 ^{6} **

**(ii) 9 ^{3} **

**(iii) 11 ^{2} **

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

**Ans:**

**(i) 2 ^{6} **= 2 x 2 x 2 x 2 x 2 x 2 = 64

**(ii) 9 ^{3} **= 9 x 9 x 9 = 729

**(iii) 11 ^{2} **= 11 x 11 = 121

**(iv) 5 ^{4} **= 5 x 5 x 5 x 5 = 625

**Q.2. Express the following in exponential form:**

**(i) 6 × 6 × 6 × 6 **

**(ii) t × t **

**(iii) b × b × b × b**

**(iv) 5 × 5× 7 × 7 × 7 **

**(v) 2 × 2 × a × a **

**(vi) a × a × a × c × c × c × c × d**

**Ans:**

(i) 6 × 6 × 6 × 6 = 6^{4}

(ii) t × t = t^{2}

(iii) b × b × b × b = b^{4}

(iv) 5 × 5× 7 × 7 × 7 = 5^{2} x 7^{3}

(v) 2 × 2 × a × a = 2^{2} x a^{2}

(vi) a × a × a × c × c × c × c × d = a^{3} x c^{4} x d

**Q.3. Express each of the following numbers using exponential notation:**

**(i) 512 **

**(ii) 343 **

**(iii) 729 **

**(iv) 3125**

**Q.4. Identify the greater number, wherever possible, in each of the following?**

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

**(ii) 5 ^{3} or 3^{5} **

**(iii) 2 ^{8} or 8^{2}**

**(iv) 100 ^{2} or 2^{100} **

**(v) 2 ^{10} or 10^{2}**

**Ans:**

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

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

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

So, 64 < 81

Hence, 3^{4} is greater than 4^{3}.

**(ii) 5 ^{3} or 3^{5} **

**5 ^{3} = 5 x 5 x 5 = 125**

**3 ^{5} = 3 x 3 x 3 x 3 x 3= 243**

So, 125 < 243

Hence, 3^{5} is greater than 5^{3}.

**(iii) 2 ^{8} or 8^{2}**

**2 ^{8} = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256**

**8 ^{2} = 8 x 8 = 64**

So, 256 > 64

Hence, 2^{8 }is greater than 8^{2 } .

**(iv) 100 ^{2} or 2^{100} **

**100 ^{2} = 100 x 100 = 10000**

**If we take , 2 ^{10} = 2x2x2x2x2x2x2x2x2x2= 1024. Which means 2^{100} is very large than 100^{2}.**

So, 100^{2} < 2^{100}

Hence, 2^{100 }is greater than 100^{2 }

**(v) 2 ^{10} or 10^{2}**

**2 ^{10} = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024**

**10 ^{2} = 10 x 10= 100**

So, 2^{10} > 10^{2}

Hence, 2^{10 }is greater than 10^{2 } .

**Q.5. Express each of the following as product of powers of their prime factors:**

**(i) 648 **

**(ii) 405 **

**(iii) 540 **

**(iv) 3,600**

**Q.6. Simplify:**

**(i) 2 × 10 ^{3} **

**(ii) 7 ^{2} × 2^{2} **

**(iii) 2 ^{3} × 5 **

**(iv) 3 × 4 ^{4}**

**(v) 0 × 10 ^{2} **

**(vi) 5 ^{2} × 3^{3} **

**(vii) 2 ^{4} × 3^{2} **

**(viii) 3 ^{2} × 10^{4}**

**Ans:**

**(i) 2 × 10 ^{3} **

= 2 x 10 x 10 x 10

= 2 x 1000 = 2000

**(ii) 7 ^{2} × 2^{2} **

** **= 7 x 7 x 2 x 2

= 49 x 4 = 196

**(iii) 2 ^{3} × 5 **

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

= 8 x 5

= 40

**(iv) 3 × 4 ^{4}**

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

= 3 x 256

= 768

**(v) 0 × 10 ^{2} **

** **= 0 x 10 x 10

= 0 x 100

= 0

**(vi) 5 ^{2} × 3^{3} **

= 5 x 5 x 3 x 3 x 3

= 25 x 27

= 675

**(vii) 2 ^{4} × 3^{2} **

= 2 x 2 x 2 x 2 x 3 x 3

= 16 x 9

= 144

**(viii) 3 ^{2} × 10^{4}**

= 3 x 3 x 10 x 10 x 10 x 10

= 9 x 10000

= 90000

**Q.7. Simplify:**

**(i) (– 4) ^{3} **

**(ii) (–3) × (–2) ^{3} **

**(iii) (–3) ^{2} × (–5)^{2} **

**(iv) (–2) ^{3} × (–10)^{3}**

**Ans:**

**(i) (– 4) ^{3} **

= (- 4) x ( – 4) x (- 4) = – 64

**(ii) (–3) × (–2) ^{3} **

= (- 3) x (- 2) x (- 2) x (- 2)

= (- 3) x (– 8) = 24

**(iii) (–3) ^{2} × (–5)^{2} **

= (-3) x (-3) x (-5) x (-5)

= 9 x 25 = 225

**(iv) (–2) ^{3} × (–10)^{3}**

= (- 2) x (- 2) x (- 2) x (-10) x(-10) x (-10)

= (- 8) x (–1000) = 8000

**Q.8. Compare the following numbers:**

** (i) 2.7 × 10 ^{12}; 1.5 × 10^{8} **

**(ii) 4 × 10 ^{14}; 3 × 10^{17}**

**Ans:**

**(i) 2.7 × 10 ^{12}; 1.5 × 10^{8} **

On comparing the exponents of base 10,

2.7 x 10^{12} > 1.5 x10^{8}

**(ii) 4 × 10 ^{14}; 3 × 10^{17}**

On comparing the exponents of base 10,

4×10^{14 }< 3×10^{17}