Prove a^ma^n = a^(m+n)
prove that aman = am+n
Posted in Algebra, asked by isaac, 6 years ago. 9544 hits.
4 Answers
(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
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Accepted Answer
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)
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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
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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 - 6 years ago
Ask Venkat Nagendra Thati for further help.
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