Students can Download Maths Chapter 10 Exponents Additional Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka State Syllabus Class 8 Maths Chapter 10 Exponents Additional Questions

Question 1.

Mark the correct option.

(a) The value of (3^{m})^{n}, for every pair of integers (m, n) is

A. 3^{m+n
}B. 3^{mn}

C. 3m^{n}

D. 3^{m} + 3^{n}

Solution:

(B) 3^{mn}

(b) If x, y, 2x + \(\frac{\mathbf{y}}{2}\) are non-zero real numbers then \(\left(2 x+\frac{y}{2}\right)^{-1}\left[(2 x)^{-1}+\left(\frac{y}{2}\right)^{-1}\right]\) equals.

A. 1

B. x . y^{-1}

C. x^{-1} . y

D. x^{-1} . y^{-1}

Solution:

(D) x^{-1} . y^{-1}

(c) If 2^{x} – 2^{x-2} = 192 the value of x is

A. 5

B. 6

C. 7

D. 8

Solution:

(D) 8

(d) The number\(\left[6^{\left(6^{6}\right)}\right]^{\frac{1}{6}}\) is equal to

A. 6^{6}

B. 6^{6 }– 1

C. 6(6^{5})

D. \(6^{6^{5}}\)

Solution:

(C) 6(6^{5})

(e) The number of pairs of positive integers (m, n) such that m^{n} = 25 is

A. 0

B. 1

C. 2

D. More than 2

Solution:

(B) 1

Question 2.

The diameter of the sun is 1.4 x 109 meters and that of the earth is about 1.2678 x 10^{7} meteres. Find the approximate ratio of the diameter of the sun to that of the earth.

Solution:

= 1.10427 x 10^{9-7}

= 1.10427 x 10^{2}

= 1.10427 x 100 = 110 . 427

∴ The ratio is 110 . 427 : 1

Question 3.

Find the value of each of the following expressions

(a) (-0.75)^{3} + (0.3)^{-3} – \(\left(-\frac{3}{2}\right)^{-3}\)

Solution:

(b)

Solution:

(c)

Solution:

Question 4.

How many digits are there in the number 2^{3} x 5^{5} x 20^{5}?

Solution:

2^{3} x 5^{5} x 20^{5}

= 8 x 625 x 3200000 = 5000 x 32

= 16000000000

∴ The number has 11 digits.

Question 5.

If a7 = 3 find the of

Solution:

Question 6.

If 2^{m}. a^{2} = 2^{8} where a, m are positive integers find all possible values of a + m.

Solution:

2^{m} . a^{2} = 2^{8}

2^{m} . a^{2} = 2^{6} . 2^{2}

∴m = 6 and a = 2

a + m = 6 + 2 = 8

Question 7.

Suppose 3^{k} x b^{2} = 6^{4} for some positive integers k and b. Find all possible values of k + b.

Solution:

3^{k} x b^{2} = 6^{4}

= (3 x 2)^{4}

= 3^{4} x 2^{4} = 3^{4} x 2^{2×2} = 34 x (2^{2})^{2}

= 3k x b^{2} = 3^{4} x 4^{2}

∴ k = 4 and b = 4

k + b = 4 + 4 = 8

Question 8.

Find the value of \(\frac{(625)^{6.25} \times(25)^{2.60}}{(625)^{7.25} \times(5)^{1.20}}\)

Solution:

Question 9.

A person had some rupees which is a power of 5. He gave a part of it to his friend which is also a power of 5. He was left with Rs. 500. How much did money he have?

Solution:

The powers of 5 are 5^{1} = 5, 5^{2} = 25, 5^{3}

= 125, 5^{4} = 625,

5^{5} = 3125 etc.

We find that 625 – 125 = 500

∴ The money with him was Rs. 625.