Question 816550
{{{(3^(-1)X^(3)Y^(-5))(3^(-1)Y^(-2))^-2 }}}
According to the order of operations (aka PEMDAS) we should start with the exponents (since nothing can be done within either set of parentheses). To raise the expression to the -2 power we use a rule for exponents, {{{(ab)^n = a^n * b^n}}}, which tells us that raising a multiple-factor term to a power, you raise each factor to that power:
{{{(3^(-1)X^(3)Y^(-5))(3^(-1))^(-2)(Y^(-2))^-2 }}}
To raise the powers of a power we use another rule for exponents, {{{(a^n)^m = a^(n*m)}}}:
{{{(3^(-1)X^(3)Y^(-5))(3^2)(Y^4) }}}
All that is left is multiplying. For this we use another rule for exponents, {{{a^n * a^m = a^(n+m)}}}. We will use this on the 3's and the Y's:
{{{3^((-1)+2)X^(3)Y^((-5)+4) }}}
which simplifies to:
{{{3^(1) X^(3)Y^(-1) }}}
or
{{{3x^3/y}}}<br>
P.S. While the {{{(ab)^n = a^n * b^n}}} property may look like a Distributive Property, it is not.