How To Solve: Exponents : Quantitative

How To Solve: Exponents

Attached pdf of this Article as SPOILER at the top! Happy learning!

Hi All,

I have recently uploaded a video on YouTube to discuss Exponents in Detail:




Following is covered in the video

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¤ Adding exponents with same base and power
¤ is ALWAYS divisible by x-y
¤ is divisible by x+y when n is even
¤ is divisible by x+y when n is odd
¤ is NEVER divisible by x-y

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= - 1 (for all odd values on n)
= + 1 (for all even values of n)

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= 1 if n is 0
= +ve if n is even (except n = 0)
= -ve if n is odd
= 0 if k=0 and n≠0
= not defined if k=0 and n=0

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= 0 , for all n ≠ 0

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= 1 ( Always)

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=

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If the base of two exponents is same and if we are multiplying the exponents, then we can keep the same base and add the powers.



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If the base of two exponents is same and if we are dividing the exponents, then we can keep the same base and subtract the powers.



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If the power of two exponents is same and if we are multiplying the exponents, then we can multiply the bases and keep the same power



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Adding exponents with same base and power

If we are adding two or more exponents with the same power, then we can add them like normal variables



is ALWAYS divisible by x-y

Ex: If we take n = 2 then we have, = = ( x - y ) * ( x + y) = divisible by x - y

is divisible by x+y when n is EVEN

Ex: If we take n = 1 then we have, = = ( x - y ) => NOT divisible by x + y
Ex: If we take n = 2 then we have, = = ( x - y ) * ( x + y) => divisible by x + y

is divisible by x+y when n is ODD

Ex: If we take n = 2 then we have, = => there is NO way in which we can express this as (x+y) * some other integer => NOT divisible by x + y
Ex: If we take n = 3 then we have, = = ( x + y ) * ( ) => divisible by x + y

is NEVER divisible by x-y

Ex: If we take n = 2 then we have, = => there is NO way in which we can express this as (x-y) * some other integer => NOT divisible by x - y
Ex: If we take n = 3 then we have, = = ( x + y ) * ( ) => there is NO way in which we can express this as (x-y) * some other integer => NOT divisible by x - y

Hope it helps!
Good Luck!