Indices
Class 8th Mathematics (old) MHB Solution
- Fill in the blanks in the following statements. (1) a x a x a x a x a x a = a…
- Simplify. (1) 5^4 × 5^3 (2) 7^8 ÷ 7^3 (3) 47^0 (4) (11 × 4)^2 (5) (2^3)^5 (6)…
Exercise 49
Question 1.Fill in the blanks in the following statements.
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
Answer:
(1) There are 6 ‘a’ which are multiplied
So the answer will be 6
(2) When two numbers with same base is multiplied then their powers are added.
In this problem the base is ‘a’ and the powers are m and n
The answer is ‘m + n’
(3) When the product of 2 numbers are raised to the same power then the individual numbers are also raised to the same power.
So the answer is ‘ m , m ’
(4) When one power is raised to another power then the resulting powers are multiplied
The answer is m × n
(5) When two numbers with the same base are divided then the powers of the numerator and denominator are subtracted.
Answer is m-n
(6) Any real number which is raised to the power 0 is always 1
Answer is 1
(7) When we take the reciprocal of a number then the sign of their power gets changed.
So the answer is m
Question 2.
Simplify.
(1) 54× 53 (2) 78 ÷ 73
(3) 470 (4) (11 × 4)2
(5) (23)5 (6) 3–4
(7) 
(8) 
(9) 
(10) 
Answer:
(1) The bases of the two numbers are same so their powers are going to be added.
54× 53 = 54 + 3
⇒ Answer: 57
(2) When two numbers with the same base are divided then the powers of the numerator and denominator are subtracted
Answer: 75
(3) Any real number which is raised to the power 0 is always 1
Answer is 1
(4) When the product of 2 numbers are raised to the same power then the individual numbers are also raised to the same power
(11× 4)2 = 112 × 42
(5) When one power is raised to another power then the resulting powers are multiplied
Answer is 215
(6) A negative power indicates the reciprocal of this number would give a positive power
Answer 
(7) The bases of the two numbers are same so their powers are going to be added
Answer 
(8) Any fraction of two real numbers which is raised to the power 0 is always 1
Answer is 1
(9) When a whole fraction is raised to some power then the numerator and denominator of that fraction are also raised to the same power
(10) When one power is raised to another power then the resulting powers are multiplied
Answer 
Exercise 50
Question 1.Write the meaning of the following index numbers.
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
Answer:
(1) The index number or power represents square root of 36
(2) The index number or power represents cube root of 27
(3) The index number or power represents square root of 17
(4) The index number or power represents cube root of 20
(5) The index number or power represents fourth root of 256
(6) The index number or power represents fifth root of 1
(7) The index number or power represents fifth root of 10
(8) The index number or power represents the sixth root of 45
Question 2.
Evaluate.
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
(9) 
(10)
Answer:
(1) On performing prime factorization on 4 we would get 22
Answer : 2
(2) On performing prime factorization on 125 we would get 53
Answer : 5
(3) When 1 is raised to any real number or fraction the result is always 1.
Answer: 1
(4) When 1 is raised to any real number or fraction the result is always 1.
Answer: 1
(5) On prime factorization of 100 we will get 52 × 22
Answer: 5× 2 = 10
(6) On prime factorization of 1000 we will get 53 × 23
Answer: 5× 2 = 10
(7) Prime factorizing 225 we get 52 × 32
Answer: 5× 3 = 15
(8) On performing prime factorization on 512 we would get 29
Answer : 23 = 8
(9) On performing prime factorization on 64 we would get 26
Answer : 23 = 8
(10) On performing prime factorization on 64 we would get 26
Answer : 2
Exercise 51
Question 1.Simplify.
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
(9) 
(10) 
(11) 
(12) 
(13) 
(14) 
(15) 
Answer:
(1) When two numbers with same base is multiplied then their powers are added
Answer: 
(2) When two numbers with the same base are divided then the powers of the numerator and denominator are subtracted
Answer: 
(3) When one power is raised to another power then the resulting powers are multiplied
Answer: 
(4) When the product of 2 numbers are raised to the same power then the individual numbers are also raised to the same power
(5) When two numbers with the same base are divided then the powers of the numerator and denominator are subtracted
Answer: 
(6) When the product of 2 numbers are raised to the same power then the individual numbers are also raised to the same power
(7) When one power is raised to another power then the resulting powers are multiplied
Answer: 
(8) When one power is raised to another power then the resulting powers are multiplied
Answer: 
(9) When two numbers with same base is multiplied then their powers are added
Answer: p
(10) When two numbers with same base is multiplied then their powers are added
Answer: 
(11) When the product of 2 numbers are raised to the same power then the individual numbers are also raised to the same power
(12) When the product of 2 numbers are raised to the same power then the individual numbers are also raised to the same power
(13) When two numbers with the same base are divided then the powers of the numerator and denominator are subtracted
Answer: 
(14) When two numbers whose base and powers are same are divided then the resulting number is 1
(15) When two numbers are divided and raised to the same power then the individual numbers are also raised to the same power
