True/False Statement (word problem)

[gio]

Hello Everyone,

I have another question. This is shorter than the last question. I hope everyone can help me. Thank you

Problem:

Write an equation for the following statement. Tell whether the equation is true or false.
The negative/opposite of x raised to the negative/opposite of y is the same as x raised to the y.

Thank you in advance. God bless you all.

 

[Loren]

The negative/opposite of x raised to the negative/opposite of y is the same as x raised to the y.

Experiment a little.

x=3 y=2 \(\displaystyle (-3)^{-2} = 3^2?\).

x=2 y=3 \(\displaystyle (-2)^{-3} = 2^3?\)

Can you draw a tentative conclusion?

 

[gio]

Hi Loren,

Once again thank you for helping me in this problem. I did get a tentative conclusion and that is that the statement is FALSE. But my next question is, what does it mean the negative/opposite of x, and the negative/opposite of y. I mean, I could have try the following:

X = 3
Y = 4

-3^-4 IS NOT equal to 3^4 This is when the numbers are negative which makes the statement FALSE, so when they are the opposite does that mean when the numbers are positive? If that is the case, then the following will be TRUE

X = 3
Y = 4

3^4 IS EQUAL to 3^4 This is when the numbers are the opposite.


I am not sure if that's what it means but from the first example I can see that the statement is FALSE.