# Simplify the expression

• March 16th 2008, 02:15 PM
mt_lapin
Simplify the expression
$(18x^3y^4)^{-1}(3x^4y)^4$

The answer I came up with was: $54x^{13}y$
but I feel this answer is incorrect. Please, what is the correct answer and how does one get it?

• March 16th 2008, 02:24 PM
Moo
Hello,

There are three main things to do :

- $(a^b)^c = a^{bc}$
- $a^b a^c = a^{b+c}$
- $(ab)^c = a^c b^c$

And note that 18 is 3²*2
• March 16th 2008, 02:30 PM
topher0805
$
(18x^3y^4)^{-1}(3x^4y)^4
$

Recall that $(18x^3y^4)^{-1} = \frac {1}{(18x^3y^4)}$

So you would have:

$\frac {81x^{16}y^4}{18x^3y^4}$

Factor out a 9:

$\frac {9x^{16}y^4}{2x^3y^4}$

Factor out an $x^3$:

$\frac {9x^{13}y^4}{2y^4}$

Factor out a $y^4$:

$\frac {9x^{13}}{2}$