Question

if x and y are integers such that x^y=1, and xy=1, then y^x=?
-1or
0
or
1 or
1.5 or
2

Answer 1

Since xy = 1, neither x nor y can be zero.

Answer 2

x^y = 1, but y is not zero, so x must be 1.

Answer 3

Since x = 1, and xy = 1, y must be 1.

Answer 4

Therefore y^x = 1.

Answer 5

yes, x and y both are 1. I tried to solve it algebrically, using indices rules.
thank u all

Answer 6

mathstudent55, can u solve it algebrically?

Answer 7

Algebraically:

Since xy = 1, x and y are reciprocals.

Therefore, y = 1/x

Substituting in x^y = 1, we get

\( \Large x^{\frac{1}{x}} = 1 \)

\( \Large \log x^{\frac{1}{x}} = \log 1 \)

\( \Large \dfrac{1}{x} \log x = 0 \)

\(\large \log x = 0\)

\(\large x = 1\)

Once you have x = 1, y = 1/x = 1/1 = 1.

Answer 8

thanks a lot.

Answer 9

You're welcome.