SCERT AP 7th Class Maths Solutions Pdf Chapter 8 Exponents and Powers Ex 8.1 Textbook Exercise Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 8th Lesson Exponents and Powers Ex 8.1

Questions 1.

Express the following into the exponential form:

(i) 14 × 14 × 14

Answer:

14 × 14 × 14 = 143

(ii) 25 × 25 × 25 × 25 × 25

Answer:

25 × 25 × 25 × 25 × 25 = 25

(iii) ab × ab × ab × ab

Answer:

ab × ab × ab × ab = (ab)^{4}

(iv) 7 × p × p × q

Answer:

7 × p × p × q = 7 × p^{2} × q

Question 2.

Express the following into expanded form:

(i) 27^{6}

Answer:

27^{6} = 27 × 27 × 27 × 27 × 27 × 27

(ii) 101^{5}

Answer:

1015 = 101 × 101 × 101 × 101 × 101

(iii) (2b)^{4}

Answer:

2b^{4} = 2b × 2b × 2b × 2b

(iv) 3a^{8}

Answer:

3a^{8} = 3 × a× a × a × a × a × a × a × a

Question 3.

Express the following In exponential form through prime factorisation: .

(i) 81

Answer:

81 = 3 × 27

= 3 × 3 × 9

= 3 × 3 × 3 × 3

∴ 81 = 3^{4}

(ii) 125

Answer:

125 = 5 × 25

= 5 × 5 × 5

∴ 125 = 5^{3}

(iii) 324

Answer:

324 = 2 × 162

= 2 × 2 × 81

= 2 × 2 × 3 × 11

= 2 × 2 × 3 × 3 × 9

= 2 × 2 × 3 × 3 × 3 × 3

∴ 324 = 2^{2} × 3^{4}

(iv) 1080

Answer:

1080 = 2 × 540

= 2 × 2 × 270

= 2 × 2 × 2 × 135

= 2 × 2 × 2 × 3 × 45

= 2 × 2 × 2 × 3 × 3 × 15

= 2 × 2 × 2 × 3 × 3 × 3 × 5

∴ 1080 = 2^{3} × 3^{1} × 5^{1}

Question 4.

Compute and identify the greater num-ber in the following pairs : 7

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

Answer:

2^{5} = 2 × 2 × 2 × 2 × 2 = 32

5^{2} = 5 × 5 = 25

32 > 25

Therefore, 2^{5} > 5^{2}

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

Answer:

7^{3} = 7 × 7 × 7 = 343

3^{7} = 3 × 3 × 3 × 3 × 3 × 3 × 3 = 2187

2187 > 343

Therefore, 3^{7} > 7^{3}

(iii) 2^{3} or 3^{2}

Answer:

2^{3} = 2 × 2 × 2 = 8

3^{2} = 3 × 3 = 9

9 > 8

Therefore, 3^{2} > 2^{3}

Question 5.

Expand 3^{3} × 4^{2} and 4^{3} × 3^{2}. Are they equal? Justify.

Answer:

3^{3} × 4^{2} = 3 × 3 × 3 × 4 × 4

= 27 × 16 = 432

4^{3} × 3^{2} = 4 × 4 × 4 × 3 × 3

= 64 × 9 = 576

432 × 576 (They are not equal)

Therefore, 576 > 432

So, 4^{3} × 3^{2} > 3^{3} × 4^{2}

Question 6.

Express the following numbers in exponential form with the given base.

(i) 1000, base 10

Answer:

∴ 1000 = 10 × 10 × 10 = 10^{3}

(ii) 512 base 2

Answer:

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

∴ 512 = 2^{9}

(iii) 243 base 3

Answer:

243 = 3 × 3 × 3 × 3 × 3

∴ 243 = 3^{5}

Question 7.

If a = 2, b = 3 find the value of

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

Answer:

Given a = 2, b = 3

a^{a} + b^{b} = 2^{2} + 3^{3}

= (2 × 2) + (3 × 3 × 3)

= 4 + 27 = 31

Therefore, if a = 2, b = 3 then a^{a} + b^{b} = 31

(ii) a^{b} + b^{a}

Answer:

Given a = 2, b = 3

a^{b} + b^{a} = 2^{3} + 3^{2}

= (2 × 2 × 2) + (3 × 3).

= 8 + 9 = 17

Therefore, if a = 2, b = 3

then a^{b} + b^{a} = 17

(iii) (a + b)^{b}

Answer:

Given a = 2, b = 3

(a + b)^{b} = (2 + 3)^{3} = 5^{3}

= 5 × 5 × 5 = 125

Therefore, if a = 2, b == 3

then (a + b)^{b} =125

Question 8.

Write the following in Exponential form:

(i) The speed of light in vacuum is about 30,00,00,000 m/sec.

Answer:

Given the speed of light = 30,00,00,000 m/sec

= 3 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10

∴ Speed of light = 3 × 10^{8} m/sec.

(ii) The population of India is about 121,00,00,000 as per 2011 census.

Answer:

Given population of India

= 121,00,00,000

= 121 × 10 × 10 × 10 × 10 × 10 × 10 × 10

= 11 × 11 × 10^{7}

∴ Population of India = 11^{2} × 10^{7} as per 2011 census.