How do you simplify #(20x^5)/y^2 * ((x^2y^2)/(2x))^3#?
First of all, expand the power of the second factor: since the power of a fraction is the power of the numerator divided by the power of the denominator, we have that
Now, the power of a product is again the power of every single factor, so
The last rule we need is the one which states that when we deal with the power of a power, we must multiplicate the exponents:
The result is thus
Now we're ready to multiply and cross simplify:
So, we can simplify
So, we're left with