Solve frac{(3x^{2}y)^{2}*(xy^{2})^{3}}{(x^3y^2)^2*y^4}

$$\frac { ( 3 x ^ { 2 } y ) ^ { 2 } \cdot ( x y ^ { 2 } ) ^ { 3 } } { ( x ^ { 3 } y ^ { 2 } ) ^ { 2 } \cdot y ^ { 4 } }$$

Evaluate

$$9x$$

Solution Steps

Expand \left(3x^{2}y\right)^{2}.

$$\frac{3^{2}\left(x^{2}\right)^{2}y^{2}\left(xy^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}x^{4}y^{2}\left(xy^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{4}y^{2}\left(xy^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

Expand \left(xy^{2}\right)^{3}.

$$\frac{9x^{4}y^{2}x^{3}\left(y^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{9x^{4}y^{2}x^{3}y^{6}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{9x^{7}y^{2}y^{6}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{9x^{7}y^{8}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

Expand \left(x^{3}y^{2}\right)^{2}.

$$\frac{9x^{7}y^{8}}{\left(x^{3}\right)^{2}\left(y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{9x^{7}y^{8}}{x^{6}\left(y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9x^{7}y^{8}}{x^{6}y^{4}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{9x^{7}y^{8}}{x^{6}y^{8}}$$

Cancel out x^{6}y^{8} in both numerator and denominator.

$$9x$$

Expand

$$9x$$

Solution Steps

Expand \left(3x^{2}y\right)^{2}.

$$\frac{3^{2}\left(x^{2}\right)^{2}y^{2}\left(xy^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}x^{4}y^{2}\left(xy^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{4}y^{2}\left(xy^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

Expand \left(xy^{2}\right)^{3}.

$$\frac{9x^{4}y^{2}x^{3}\left(y^{2}\right)^{3}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{9x^{4}y^{2}x^{3}y^{6}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{9x^{7}y^{2}y^{6}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{9x^{7}y^{8}}{\left(x^{3}y^{2}\right)^{2}y^{4}}$$

Expand \left(x^{3}y^{2}\right)^{2}.

$$\frac{9x^{7}y^{8}}{\left(x^{3}\right)^{2}\left(y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{9x^{7}y^{8}}{x^{6}\left(y^{2}\right)^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{9x^{7}y^{8}}{x^{6}y^{4}y^{4}}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{9x^{7}y^{8}}{x^{6}y^{8}}$$

Cancel out x^{6}y^{8} in both numerator and denominator.

$$9x$$