4xy to the 2nd times 4x to the 3rd

Question

ipwnbunnies · Answer

$$(4xy)^{2}(4x)^{3}$$

ipwnbunnies · Answer

I suggest expand everything out, apply the power of each variable. Then combine the variables

ipwnbunnies · Answer

$$x^{a} * x^{b} = x^{a+b}$$

ipwnbunnies · Answer

$$(x^{a})^{b} = x^{a*b}$$

ipwnbunnies · Answer

Soooo, It'll look like this expanded
$$4^{2}*x^{2}y^{2}*4^{3}x^{3}$$

anonymous · Answer

Is the whole 4xy put to the second if it is not in parenthesis, or just the y?

ipwnbunnies · Answer

It depends on your problem. Can you rewrite the expression using parentheses?

ipwnbunnies · Answer

If 4xy isn't in parentheses, then the 'to the second' would only apply to y

ipwnbunnies · Answer

Is it this?
$$4xy^{2}(4x)^{3}$$

anonymous · Answer

I can't seem to get my exponents right, but what you wrote is correct except there is no parenthesis around the 4x to the 3rd

ipwnbunnies · Answer

Ok lol. So it's this:
$$4xy^{2}*4x^{3}$$

anonymous · Answer

YES! :)

ipwnbunnies · Answer

Alright, this makes the problem easier! Just follow one of the properties of exponents I showed you.
$$x^{a} * x^{b} = x^{a+b}$$

ipwnbunnies · Answer

The x can also be a y. It's just the general form of the property.

ipwnbunnies · Answer

For the two 4's, you multiply them together like regular numbers. Tell me what you get.

anonymous · Answer

So, it's 4 x 4 = 16; then x to the 4th and y to the 2nd.  Something like 16x to the 4th, y to the 2nd?

ipwnbunnies · Answer

Correct! Great job man. :)

anonymous · Answer

Thank you so much!  Have a great one!