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 × 10^{9}

(iii) 48300000

Solution:

= 483 × 100000 = 483 × 10^{5}

(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 × 10^{5}

Solution:

= 4.37 × 100000

= 437000

(ii) 5.8 × 10^{7}

Solution:

= 5.8 × 10000000

(iii) 32.5 × 10^{-4}

Solution:

= \(\frac{32.5}{10^{4}}=\frac{32.5}{10000}\)

= 0.00325

(iv) 3.71529 × 10^{7}

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 × 10^{8} m/sec

(iv) The distance between the moon and the earth is 384467000 m(app)

Solution:

= 384467 × 1000 m

= 384467 × 10^{3}

(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 × 10^{2} 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} × a^{n} = a^{m + n} ]

= x^{-5} = x^{-6}

= -5 = -6(False)

∴ In this case do not agree with Rakesh solution.

(ii) \(\frac{X^{3}}{X^{2}}\) = x^{4}

Solution:

⇒ x^{3-2} = x^{4} [∵ \(\frac{a^{m}}{a^{n}}\) = a^{m – n} ]

⇒ x^{1} = x^{4}

[∵Here bases are equal, so exponents are also equal]

⇒ 1 = 4 (It is false)

∴ I do not agree with Rakesh solution.

(iii) (x^{2})^{3} = (x^{2})^{3} = x^{8}

Solution:

(x^{2})^{3} = \(x^{2^{3}}\) = x^{8}

⇒ (x^{2})^{3} = \(x^{2^{3}}\)

⇒ x^{2 × 3} = \(x^{2^{3}}\)

⇒ x^{6} = x^{2 × 2 × 2}

⇒ x^{6} = x^{8}

[∵ 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 = \(\frac{x}{x}\)

⇒ x^{0} = 9

⇒ 1 = 9

It is false

∴ I don’t agree with Rakesh solution.