# Thread: Exponents - Simplifying

1. ## Exponents - Simplifying

Simplify:

Note: \uparrow means "to the power of"

(2xy\uparrow 3)\uparrow 2 (xy)\uparrow 3

2. Is it this:

$(2xy^{3})^{2}(xy)^{3}?$

If so, what have you tried so far?

3. Yes it is that. I have tried distributing the 2 to 2x and y. Then distributing the 3 to the x and the y.

Which got me this:
(2x{2} y{5})(x{3} y{3})
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(4x y{5}) (x{3} y{3})

Then I multiplied the first parenthesis by the second parenthesis:
And I got this:

4x{6}y{15}

I checked at the back of my textbook but the answer is wrong.

4. Exponents multiply in some situations, and add in others. You have, for example,

$(x^{2})^{3}=x^{2}x^{2}x^{2}=x^{2\times 3}=x^{6}.$

So they multiply in that circumstance. If I just have

$x^{2}x^{3}=x^{5},$

then they add. Do not confuse those two situations!

You have made an error along these lines in your calculations. Try doing it again, with these rules in mind.

5. $\left(2xy^3)^2=4x^2y^6$