Q. 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


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