Question 22386
a. {{{(x^10 * y^3)/(x^4 * y^5) }}}
When you divide with the same base number, you subtract exponents.
{{{x^6*y^(-2)}}} 


When you have a negative exponent such as {{{y^(-2)}}} it becomes a fraction whose numerator is 1, and the denominator is {{{y^2}}} or {{{1/(y^2) }}}
{{{x^6 *(1/(y^2)) }}}
{{{(x^6)/(y^2)}}}


b. {{{((p^4 * q^5)/(r^3))^2 }}}
When you raise a power to a power, you multiply the exponents:
{{{ (p^8 *q^10)/(r^6) }}}


c. {{{ (108r^2 * y)/(9r^3 * y^2) }}}
Rewrite the fraction into three fractions:
{{{(108/9)*(r^2/r^3)*(y/(y^2)) }}}
{{{(12)*(1/r)* (1/y) }}}
{{{12/(ry)}}}


d. {{{(3x^2 * y^2) * (-5x * y^4)^2 }}}
Square everything in the second parentheses:
{{{(3x^2 *y^2) *(25*x^2*y^8) }}}
When you multiply with the same base number, you add exponents:
{{{75x^4y^10 }}}


R^2 at SCC