(3x)^3 y^4 / 3x^4 y^3 evaluate or solve

So you have:

(3x)^3 (y)^4
-----------------
(3x)^4 (y)^3

When you have exponents to the same common variable OVER each other, you can treat it like a subtraction problem, as followed:

(3x)^3 - (3x)^4 = (3x)^-1

and

y^4 - y^3 = y^1 = y (because any variable to the power of 1 equals that variable)

So now you have:

(3x)^-1 (y)

To be simplified completely, you need to get rid of that negative exponent. To do this, simply move it to the denominator. So now you have:

1(y)
-------
(3x)^1

1 x y = y and as we did before, (3x)^1 = 3x

So your final answer is:

1/3x

(3x)^3 y^4 / 3x^4 y^3

SOLUTION

= 3^3(x)^3. y^4/ 3x^4. y^3

Cancel common terms,

=3^2.y /x

=9y/x

[size=150]Hi Ferra[/size]

This is a great effort Ferra, and I really like to see people 'having a go' but there are a few problems with your solution.

Ferra:

So you have:

(3x)^3 (y)^4
-----------------
(3x)^4 (y)^3 There is no bracket around the 3x in the denominator NOR is there any bracket around 3x^4 y^3 so why do you think that this is the question.

It may well be the intended question but it is not the question asked.

When you have exponents to the same common variable OVER each other, you can treat it like a subtraction problem, as followed:

(3x)^3 - (3x)^4 = (3x)^-1

and

y^4 - y^3 = y^1 = y (because any variable to the power of 1 equals that variable)

So now you have:

(3x)^-1 (y)

To be simplified completely, you need to get rid of that negative exponent. To do this, simply move it to the denominator. So now you have:

1(y)
-------
(3x)^1

1 x y = y and as we did before, (3x)^1 = 3x
-----------------------------------------------------------------------
So your final answer is:

1/3x

You have also forgotten the y so the answer to your question is y/(3x)

*
[size=150]Hi Demogorgon[/size]

Demogorgon:

(3x)^3 y^4 / 3x^4 y^3

SOLUTION

= 3^3(x)^3. y^4/ [3x^4. y^3]

Cancel common terms,

=3^2.y /x

=9y/x

This is a good answer Demogorgon.
You have made an assumption about what the intended question was. You may be right about the intention but it is not actually the question that is written.
I will show you what I mean in my last post.

Guest:

(3x)^3 y^4 / 3x^4 y^3

This may not be the answer to the intended question BUT it is the answer to the question asked.

[(3x) ³ y ⁴ / 3 ] * x ⁴ y ³

[3 ³x ³ y ⁴ / 3 ] * x ⁴ y ³

[3 ²x ³ y ⁴ ] * x ⁴ y ³

9x ⁷ y ⁷