# AP Board 8th Class Maths Solutions Chapter 4 Exponents and Powers Ex 4.2

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 4 Exponents and Powers Ex 4.2 Textbook Questions and Answers.

## AP State Syllabus 8th Class Maths Solutions 4th Lesson Exponents and Powers Exercise 4.2 Question 1.
Express the following numbers in the standard form.
(i) 0.000000000947
Solution:
= $$\frac{947}{1000000000000}$$ = 947 × 10-12

(ii) 543000000000
Solution:
= 543 × 1000000000 = 543 × 109

(iii) 48300000
Solution:
= 483 × 100000 = 483 × 105 (iv) 0.00009298
Solution:
= $$\frac{9298}{100000000}$$
= 9298 × 10-8

(v) 0.0000529
Solution:
= $$\frac{529}{10000000}$$
= 529 × 10-7

Question 2.
Express the following numbers in the usual form.
(i) 4.37 × 105
Solution:
= 4.37 × 100000
= 437000

(ii) 5.8 × 107
Solution:
= 5.8 × 10000000

(iii) 32.5 × 10-4
Solution:
= $$\frac{32.5}{10^{4}}=\frac{32.5}{10000}$$
= 0.00325 (iv) 3.71529 × 107
Solution:
= 3.71529 × 10000000
= 37152900

(v) 3789 × 10-5
Solution:
= $$\frac{3789}{10^{5}}=\frac{3789}{100000}$$
= 0.03789

(vi) 24.36 × 10-3
Solution:
= $$\frac{24.36}{10^{3}}=\frac{24.36}{1000}$$
= 0.02436

Question 3.
Express the following information in the standard form
(i) Size of the bacteria is 0.0000004 m
Solution:
= [klatex]\frac{4}{10000000}[/latex] m = 4 x 10-7 m

(ii) The size of red blood cells is 0.000007mm
Solution:
= $$\frac{7}{1000000}$$ = 7 × 10-6 (iii) The speed of light is 300000000 m/sec
Solution:
= 3 × 10,00,00,000 = 3 × 108 m/sec

(iv) The distance between the moon and the earth is 384467000 m(app)
Solution:
= 384467 × 1000 m
= 384467 × 103

(v) The charge of an electron is 0.0000000000000000016 coulombs
Solution:
= 0.0000000000000000016
= $$\frac{16}{10000000000000000000}$$
= $$\frac{16}{10^{19}}$$
= 16 × 10-19 coulombs

(vi) Thickness of a piece of paper is 0.0016 cm
Solution:
= 0.0016 cm = $$\frac{16}{10000}$$
= $$\frac{16}{10^{4}}$$
= 16 × 10-4 cm

(vii) The diameter of a wire on a computer chip is 0.000005 cm
Solution:
= 0.000005 cm = $$\frac{5}{1000000}$$ cm
= $$\frac{5}{10^{6}}$$ cm = 5 × 10-6 cm Question 4.
In a stack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of thickness 0.016mm. What is the total thickness of the stack.
Solution:
The thickness of 5 books of a pack
= (5 books × their thickness)
= 5(papers × their thickness)
= (20 mm × 5) + (0.016 mm × 5)
= 100 mm + 0.080 mm
= (100 + 0.080) mm
= 100.08 mm
= 1.0008 × 102 mm

Question 5.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
(i) x-3 × x-2 = x-6
Solution:
x-3 × x-2 = x-6
= x-3+(-2) = x-6 [∵ am × an = am + n ]
= x-5 = x-6
= -5 = -6(False)
∴ In this case do not agree with Rakesh solution. (ii) $$\frac{X^{3}}{X^{2}}$$ = x4
Solution:
⇒ x3-2 = x4 [∵ $$\frac{a^{m}}{a^{n}}$$ = am – n ]
⇒ x1 = x4
[∵Here bases are equal, so exponents are also equal]
⇒ 1 = 4 (It is false)
∴ I do not agree with Rakesh solution.

(iii) (x2)3 = (x2)3 = x8
Solution:
(x2)3 = $$x^{2^{3}}$$ = x8
⇒ (x2)3 = $$x^{2^{3}}$$
⇒ x2 × 3 = $$x^{2^{3}}$$
⇒ x6 = x2 × 2 × 2
⇒ x6 = x8
[∵ Bases are equal, so exponents are also equal]
⇒ 6 = 8
It is false
∴ Rakesh solution is wrong.

(iv) x-2 = √x
Solution:
⇒ x-2 = x1/2
⇒ -2 = 1/2 (it is false)
∴ I don’t agree with Rakesh solution. (v) 3x-1 = $$\frac{1}{3 x}$$
Solution:
⇒ 3x-1 = $$\frac{1}{3 x}$$
⇒ 3 × 3 = $$\frac{x}{x}$$
⇒ x0 = 9
⇒ 1 = 9
It is false
∴ I don’t agree with Rakesh solution.