KSEEB Solutions for Class 8 Maths Chapter 10 Exponents Additional Questions

KSEEB Solutions for Class 8 Maths Chapter 10 Exponents Additional Questions

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. 3mⁿ
D. 3^m + 3ⁿ
Solution:
(B) 3^mn

Question 4.
How many digits are there in the number 2³ x 5⁵ x 20⁵?
Solution:
2³ x 5⁵ x 20⁵
= 8 x 625 x 3200000 = 5000 x 32
= 16000000000
∴ The number has 11 digits.

Question 6.
If 2^m. a² = 2⁸ where a, m are positive integers find all possible values of a + m.
Solution:
2^m . a² = 2⁸
2^m . a² = 2⁶ . 2²
∴m = 6 and a = 2
a + m = 6 + 2 = 8

Question 7.
Suppose 3^k x b² = 6⁴ for some positive integers k and b. Find all possible values of k + b.
Solution:
3^k x b² = 6⁴
= (3 x 2)⁴
= 3⁴ x 2⁴ = 3⁴ x 2^2×2 = 34 x (2²)²
= 3k x b² = 3⁴ x 4²
∴ k = 4 and b = 4
k + b = 4 + 4 = 8

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 5¹ = 5, 5² = 25, 5³
= 125, 5⁴ = 625,
5⁵ = 3125 etc.
We find that 625 – 125 = 500
∴ The money with him was Rs. 625.