Adding Exponents

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Exponent is also known as index or power. If a certain number a is multiplied m times in succession then the continued product so obtained is called the m thpower of a and is written as a ^m (read as, a to the power m).
Thus a ^m = a x a x a x a x ………….to m factors.
Here, a is called the base of a^m and m is the exponent of a^m.
For example: - x^3 = x * x * x
And (-3)^6 = (-3) * (-3) *(-3) * (-3) * (-3) * (-3);
Here x and -3 are the base of x ^3 and (-3)^6 respectively and their exponents are 3 and 6.
In particular, a ^2 is called the square of a (or, a to the power 2) and a^3 is called the cube of a (or, a to the power 3).


 Adding exponents’ example:
Add the exponents (2x^2+3y^2+z^3) and (x^2 + y^3 + 3 z^3).
 
Solution: -
(2 x^2 + 3 y^2 + z^3 ) + (x^2 + y^2 + 3 z^3)
= (2 x^2 + x^2) + (3 y^2 + y^2) +(z^3 + 3 z^3)  (Group the like terms)
= 3 x^2 + 4 y^2 + 4 z^3

 
Another example: Add (5 x^3 + 8 x^2 + 2x) and (x ^3 + 2 x^2 + 3 x.)

Solution: -

(5 x^3 + 8 x^2 + 2x) + (x ^3 + 2 x^2 + 3 x.)
= (5 x^3 + x^3)+(8 x^2 + 2 x^2)+ (2 x + 3 x)
= 6x^ +10x^2+5x





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