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\frac{\left(3xy\right)^{2}}{2^{2}}\times 2xy^{2}
To raise \frac{3xy}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(3xy\right)^{2}\times 2}{2^{2}}xy^{2}
Express \frac{\left(3xy\right)^{2}}{2^{2}}\times 2 as a single fraction.
\frac{\left(3xy\right)^{2}}{2}xy^{2}
Cancel out 2 in both numerator and denominator.
\frac{\left(3xy\right)^{2}x}{2}y^{2}
Express \frac{\left(3xy\right)^{2}}{2}x as a single fraction.
\frac{\left(3xy\right)^{2}xy^{2}}{2}
Express \frac{\left(3xy\right)^{2}x}{2}y^{2} as a single fraction.
\frac{3^{2}x^{2}y^{2}xy^{2}}{2}
Expand \left(3xy\right)^{2}.
\frac{9x^{2}y^{2}xy^{2}}{2}
Calculate 3 to the power of 2 and get 9.
\frac{9x^{3}y^{2}y^{2}}{2}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{9x^{3}y^{4}}{2}
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.
\frac{\left(3xy\right)^{2}}{2^{2}}\times 2xy^{2}
To raise \frac{3xy}{2} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(3xy\right)^{2}\times 2}{2^{2}}xy^{2}
Express \frac{\left(3xy\right)^{2}}{2^{2}}\times 2 as a single fraction.
\frac{\left(3xy\right)^{2}}{2}xy^{2}
Cancel out 2 in both numerator and denominator.
\frac{\left(3xy\right)^{2}x}{2}y^{2}
Express \frac{\left(3xy\right)^{2}}{2}x as a single fraction.
\frac{\left(3xy\right)^{2}xy^{2}}{2}
Express \frac{\left(3xy\right)^{2}x}{2}y^{2} as a single fraction.
\frac{3^{2}x^{2}y^{2}xy^{2}}{2}
Expand \left(3xy\right)^{2}.
\frac{9x^{2}y^{2}xy^{2}}{2}
Calculate 3 to the power of 2 and get 9.
\frac{9x^{3}y^{2}y^{2}}{2}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{9x^{3}y^{4}}{2}
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.