Can someone please help me on this question or help me get started.

(2x^y+x^-y)^3
= (2x^y+x^-y)(2x^y+x^-y)(2x^y+x^-y)
= ???

Now what do I do next?

please help and thank you

8x^3y+8x^y+2x^-y+4x^y+4x^-y+x^-3y

What do I do with the exponents?

Is this correct so far?

is this the right answer?

20x^5y+7x^-5y

What do you do with the negative exponent? Do you just leave it how it is?

correct so far

all you have to do is collect your like terms
you have 8x^y + 4x^y which is 12x^y
and 2x^-y + 4x^-y which is 6x^-y

= 8x^(3y) + 12x^y + 6x^-y + y^(-3y)

To simplify the expression (2x^y + x^(-y))^3, you need to apply the distribution property and simplify each term within the parentheses.

Let's break it down step by step:

Step 1: Expand the expression using the distributive property:
(2x^y + x^(-y))^3 = (2x^y + x^(-y))(2x^y + x^(-y))(2x^y + x^(-y))

Step 2: Multiply the first term of the first parentheses by each term inside the other parentheses, then the second term by each term inside the remaining parentheses:
= (2x^y * 2x^y * 2x^y) + (2x^y * 2x^y * x^(-y)) + (2x^y * x^(-y) * 2x^y) + (2x^y * x^(-y) * x^(-y)) + (x^(-y) * 2x^y * 2x^y) + (x^(-y) * 2x^y * x^(-y)) + (x^(-y) * x^(-y) * 2x^y) + (x^(-y) * x^(-y) * x^(-y))

Step 3: Simplify each of the terms:
= 8x^(2y) + 4x^(y-y) + 4x^(2y-y) + 2x^(-2y) + 4x^(y-y) + 2x^(y-2y) + 2x^(-2y) + x^(-3y)

Simplifying further:
= 8x^(2y) + 4 + 4x^y + 2x^(-2y) + 4 + 2x^(-y) + 2x^(-2y) + x^(-3y)

So, the final simplified expression is:
8x^(2y) + 4 + 4x^y + 2x^(-2y) + 4 + 2x^(-y) + 2x^(-2y) + x^(-3y)

Note: It's important to note that x^(-n) is equivalent to 1/x^n.