Question 472189
your equation looks like this:
{{{((12x^2y^3)/(6z^5)) / ((3z^7)/(2xy))}}}
since (a/b) / (c/d) is equivalent to (a/b) * (d/c), your equation is equivalent to:
{{{((12x^2y^3)/(6z^5)) * ((2xy)/(3z^7))}}}
since (a/b) * (d/c) is equivalent to (a*d) / (b*c), then your equation is equivalent to:
{{{((12x^2y^3) * (2xy)) /((6z^5) * (3z^7))}}}
By the laws of commutation, you can reorder the terms in a multiplication.
this means that a*d*g*b is equivalent to a*b*d*g.
your equation is therefore, equivalent to:
{{{(12*2*x^2*x*y^3*y) /(6z^5 * 3z^7)}}}
since a^b * a^c = a^(b+c), then your equation is equivalent to:
{{{(24*x^3*y^4) /(18z^12)}}}
you can further simplify this to:
{{{(4*x^3*y^4) /(3z^12)}}}
to confirm your answer is correct, simply replace x, y, and z with numbers and see if the original equation and the final equation give you the same answer.
i did that by making x = 2, y = 3, z = 4 and i was able to confirm that both the original equation and the final equation gave me the same answer.