6x^3y^4 4x^2y^3 12x^3y^4 27x^2y^3 Which expression is equivalent to (36x^4y^5)/((3xy)^2) forallyalues of xand ywhere the expression is defined? Answer: square

To simplify the given expression, we can start by simplifying the denominator.<br /><br />$(3xy)^{2} = 3^{2}x^{2}y^{2} = 9x^{2}y^{2}$<br /><br />Now, we can rewrite the given expression as:<br /><br />$\frac {36x^{4}y^{5}}{9x^{2}y^{2}}$<br /><br />Next, we can simplify the fraction by dividing the numerator and denominator by their common factors.<br /><br />$\frac {36x^{4}y^{5}}{9x^{2}y^{2}} = \frac {36}{9} \cdot \frac {x^{4}}{x^{2}} \cdot \frac {y^{5}}{y^{2}}$<br /><br />Simplifying each fraction, we get:<br /><br />$\frac {36}{9} = 4$<br /><br />$\frac {x^{4}}{x^{2}} = x^{2}$<br /><br />$\frac {y^{5}}{y^{2}} = y^{3}$<br /><br />Putting it all together, we have:<br /><br />$\frac {36x^{4}y^{5}}{9x^{2}y^{2}} = 4x^{2}y^{3}$<br /><br />Therefore, the expression equivalent to $\frac {36x^{4}y^{5}}{(3xy)^{2}}$ for all values of x and y where the expression is defined is $4x^{2}y^{3}$.