Question

Explain the properties of exponents.

Answer 1

((a)^m)^n=a^mn
(a^m×b^m)=ab^m
(a^m×a^n)=a^m+n
(a^m÷b^m)=a/b^m
(a^m÷a^n)=a^m-n

Answer 2

1) a^m +a^n=a^(m-n)
This means that if two no.s having same bases but different powers when multiplied, their powers are only added.

2) a^m/a^n=a^(m-n) or. 1/a^(n-m)
This means when two no.s having the same base but different powers are divided then two things may happen:
i) the lower power is subtracted from the upper power if the upper power is greater
ii) the upper power is subtracted from the lower power if the lower power is greater leaving a numerator 1

3) (a/b)^n= a^n/b^n
This means that when a fraction has a power as a whole then the numerator and denominator both have the same power.

4) a^0 = 1
There is no specific explanation for this.

5) (a^m)^n=a^mn
This means that when an already indicised no. is given a power on basis of whole then both the powers are multiplied

6) (a×b)^m= (ab)^m
Here also the power of the terms if multiplicands is same as they are present as a whole powered no.


Hope it helps u