How do you simplify #\frac { ( 4x ^ { 3} ) ^ { 2} \cdot x ^ { - 4} } { 10x ^ { 5} }#?

1 Answer

#4x^(-3)=4/x^3#

Explanation:

Let's break this down a bit at a time. First off, we have:

#((4x^3)^2xxx^(-4))/(10x^5)#

First we can break down that square of the first term:

#((4x^(3xx2))xxx^(-4))/(10x^5)#

#(4x^6xxx^(-4))/(10x^5)#

And now let's move the denominator up to the numerator:

#4x^6xxx^(-4)xx10x^-5#

And lastly let's combine everything here:

#4x^(6-4-5)#

#4x^(-3)#

We can leave it this way or rewrite as:

#4/x^3#