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 [∵ a^m × aⁿ = a^{m + 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:
⇒ x^3-2 = x⁴ [∵ \(\frac{a^{m}}{a^{n}}\) = a^{m – 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 = \(x^{2^{3}}\)
⇒ x^{2 × 3} = \(x^{2^{3}}\)
⇒ x⁶ = x^{2 × 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 = x^1/2
⇒ -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.