Solve frac{6(xy)^{2}*3^{2}(xy)^-3}{2y^2x^-3y^-3}

$$\frac { 6 ( x y ) ^ { 2 } \times 3 ^ { 2 } ( x y ) ^ { - 3 } } { 2 y ^ { 2 } x ^ { - 3 } y ^ { - 3 } }$$

Evaluate

$$27x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{6\left(xy\right)^{-1}\times 3^{2}}{2y^{2}x^{-3}y^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{6\left(xy\right)^{-1}\times 3^{2}}{2y^{-1}x^{-3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 3^{2}\times \frac{1}{xy}}{x^{-3}\times \frac{1}{y}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{3^{3}\times \frac{1}{xy}}{x^{-3}\times \frac{1}{y}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27\times \frac{1}{xy}}{x^{-3}\times \frac{1}{y}}$$

Express 27\times \frac{1}{xy} as a single fraction.

$$\frac{\frac{27}{xy}}{x^{-3}\times \frac{1}{y}}$$

Express x^{-3}\times \frac{1}{y} as a single fraction.

$$\frac{\frac{27}{xy}}{\frac{x^{-3}}{y}}$$

Divide \frac{27}{xy} by \frac{x^{-3}}{y} by multiplying \frac{27}{xy} by the reciprocal of \frac{x^{-3}}{y}.

$$\frac{27y}{xyx^{-3}}$$

Cancel out y in both numerator and denominator.

$$\frac{27}{x^{-3}x}$$

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{27}{x^{-2}}$$

Expand

$$27x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{6\left(xy\right)^{-1}\times 3^{2}}{2y^{2}x^{-3}y^{-3}}$$

To multiply powers of the same base, add their exponents. Add 2 and -3 to get -1.

$$\frac{6\left(xy\right)^{-1}\times 3^{2}}{2y^{-1}x^{-3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 3^{2}\times \frac{1}{xy}}{x^{-3}\times \frac{1}{y}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{3^{3}\times \frac{1}{xy}}{x^{-3}\times \frac{1}{y}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27\times \frac{1}{xy}}{x^{-3}\times \frac{1}{y}}$$

Express 27\times \frac{1}{xy} as a single fraction.

$$\frac{\frac{27}{xy}}{x^{-3}\times \frac{1}{y}}$$

Express x^{-3}\times \frac{1}{y} as a single fraction.

$$\frac{\frac{27}{xy}}{\frac{x^{-3}}{y}}$$

Divide \frac{27}{xy} by \frac{x^{-3}}{y} by multiplying \frac{27}{xy} by the reciprocal of \frac{x^{-3}}{y}.

$$\frac{27y}{xyx^{-3}}$$

Cancel out y in both numerator and denominator.

$$\frac{27}{x^{-3}x}$$

To multiply powers of the same base, add their exponents. Add -3 and 1 to get -2.

$$\frac{27}{x^{-2}}$$