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AoPS Problem - Can you double check me please


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Problem 2.3.3.

 

When x = 2 and y = -2, what is the value of x to the power of x+y plus y to the power of x-y.

 

Ok, so here is what I (and my daughter) did at first. I substituted in the numbers:

 

2 to the (2+(-2)) power PLUS -2 to the (2-(-2)) power =

2 to the 0 power PLUS -2 to the fourth =

1 + (-16) =

-15

 

We were wrong because in line 2, we should have had:

2 to the 0 power PLUS (-2) to the fourth =

1 + 16 =

17

 

Ok.... so I see the issue. The negative was squared as well making the answer 16 rather than -16. So here is why I was wrong:

 

In the equation above the y was raised to the power of x+y. That is, whatever y is be it negative or positive was ALL raised to the power of x+y. When you then substitute in a negative number, you must put in the parenthesis to show that the entire number is raised. Correct?

 

This would be far less confusing if I could actually do exponents on this forum but I can't see how to. If you have your book... it would probably be easier to flip to page 76 and read the problem for yourself. Thank you!

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The usual way to do exponents in plain text is with the caret symbol ^.

 

Problem 2.3.3.

 

When x = 2 and y = -2, what is the value of x to the power of x+y plus y to the power of x-y.

 

x^(x+y) + y^(x-y)

2^(2-2) + (-2)^(2+2)

2^0 + (-2)^4

1 + 16

17

 

Ok.... so I see the issue. The negative was squared as well making the answer 16 rather than -16. So here is why I was wrong:

 

In the equation above the y was raised to the power of x+y. That is, whatever y is be it negative or positive was ALL raised to the power of x+y. When you then substitute in a negative number, you must put in the parenthesis to show that the entire number is raised. Correct?

Correct.
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