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Prove a^ma^n = a^(m+n)

prove that aman = am+n

Posted in Algebra, asked by isaac, 6 years ago. 9544 hits.

5

(a^m)*(a^n) = a^(m+n)

Proof

a^m = a*a*a*....a[here m times a is multiplied]

a^n  = a*a*a*...a[here n times a is multiplied]

(a^m)*(a^n) = {a*a*a*....a[ m times a]}*{a*a*a*...a[ n times a]}

                    = a*a*a*.........*a[m times a* n times a  = (m+n) times a]

                    = a^(m+n)

hence prooved

vinu omanan
vinu omanan - 6 years ago
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3

am * an=am+n

LHS     =RHS

forward proof, LHS=RHS...............................1

backward proof, RHS=LHS..............................2

using 1,

am = a × a × ... × a →m of these    
an= a × a × ... × a →n of these
am× an = a × a × ... × a × a × a × ... × a →(m+n) of these
    = a(m+n)

David Owino
David Owino - 6 years ago
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-1

Let us consider m=5, n=4

therefore,

am=a5

    = a x a x a x a x a

an=a4

   = a x a x a x a

therefore,

a5 x a4 = a x a x a x a x a x a x a x a x a

            = a9

Which shows m+n = 5+4 = 9

hence,

am x an = am+n

Gurudas Kadam
Gurudas Kadam - 6 years ago
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-5

given problem is a^m*a^n=a^(m+n)

 let us take L.H.S => a^m*a^n

 the base is same for two values.so base is same ,the powers will be added

now we can do that, it will become

 

=> a^(m+n)

now, L.H.S=R.H.S

Venkat Nagendra Thati
Venkat Nagendra Thati - 6 years ago
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