Question 721215
{{{x^(-6)y^3/(-27x^9y^(-3/4))}}}
If you have trouble with expressions like this, it can help to split it up into separate fractions:
{{{(1/(-27))*(x^(-6)/x^9)*(y^3/y^(-3/4))}}}
so that the coefficients, the x's and the y's are all in their own fractions. To divide the x's and y's we use the rule for exponents when dividing: Subtract the exponents:
{{{(-1/27)*(x^(-6-9))*(y^(3-(-3/4)))}}}
{{{(-1/27)*(x^(-15))*(y^(12/4-(-3/4)))}}}
{{{(-1/27)*(x^(-15))*(y^(15/4))}}}
This could be an acceptable answer. Or we could rewrite the x with a positive exponent:
{{{(-1/27)*(1/x^15)*(y^(15/4))}}}
This could be an acceptable answer. Or we could rewrite the y in simplified radical form. (A fractional exponent represents a radical.)
{{{(-1/27)*(1/x^15)*(root(4, y^15))}}}
{{{(-1/27)*(1/x^15)*(root(4, y^4*y^4*y^4*y^3))}}}
{{{(-1/27)*(1/x^15)*(root(4, y^4)*root(4, y^4)*root(4, y^4)*root(4, y^3))}}}
{{{(-1/27)*(1/x^15)*(y^3*root(4, y^3))}}}
This could be an acceptable answer. Or we could put everything back together (i.e. multiply it out):
{{{-y^3*root(4, y^3)/27x^15}}}