Question

HEY THERE PLS HELP ME: Integers as Exponents

1. explain why (-1)^n=1 for any even #
2. Explain why both 4x^0-3y^0 & (4x-3y)^0 simpifyy to 1

Answer 1

\[(-1)^{n}=1\]
for any n=even
because power means nothing but multiplication.
for e.g.
n=2
(-1)^2=(-1)*(-1)=1
similarly you can check for any other even value of n.

Answer 2

Also, anything raise to even power is always positive.
and 1 raise to power anything is always 1 itself.

Answer 3

Anything raise to power zero is always 1 because
Let us assume without the loss of generality,
a,m,n belongs to R(real numbers) and a not equal to 0.
then
\[\frac{ a ^{m} }{ a ^{n} }=a ^{m-n}\]
when m=n
\[\frac{ a ^{n} }{ a ^{n} }=a ^{n-n}\]
a^n cancels out on left side and right side becomes a^0 and it implies
\[1=a ^{0}\]
hence proved.

Answer 4

wait what do u mean by the left side and the right side