Solve frac{(2x^{3}y)^{2}*(3xy^4)^2}{(5xy^2)^2}=

$$\frac { ( 2 x ^ { 3 } y ) ^ { 2 } \times ( 3 x y ^ { 4 } ) ^ { 2 } } { ( 5 x y ^ { 2 } ) ^ { 2 } } =$$

Evaluate

$$\frac{36\left(xy\right)^{6}}{25}$$

Solution Steps

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

$$\frac{2^{2}\left(x^{3}\right)^{2}y^{2}\times \left(3xy^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

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

$$\frac{2^{2}x^{6}y^{2}\times \left(3xy^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{6}y^{2}\times \left(3xy^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

Expand \left(3xy^{4}\right)^{2}.

$$\frac{4x^{6}y^{2}\times 3^{2}x^{2}\left(y^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{4x^{6}y^{2}\times 3^{2}x^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4x^{6}y^{2}\times 9x^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

Multiply 4 and 9 to get 36.

$$\frac{36x^{6}y^{2}x^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

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

$$\frac{36x^{8}y^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{36x^{8}y^{10}}{\left(5xy^{2}\right)^{2}}$$

Expand \left(5xy^{2}\right)^{2}.

$$\frac{36x^{8}y^{10}}{5^{2}x^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{36x^{8}y^{10}}{5^{2}x^{2}y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{36x^{8}y^{10}}{25x^{2}y^{4}}$$

Cancel out x^{2}y^{4} in both numerator and denominator.

$$\frac{36x^{6}y^{6}}{25}$$

Expand

$$\frac{36\left(xy\right)^{6}}{25}$$

Solution Steps

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

$$\frac{2^{2}\left(x^{3}\right)^{2}y^{2}\times \left(3xy^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

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

$$\frac{2^{2}x^{6}y^{2}\times \left(3xy^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4x^{6}y^{2}\times \left(3xy^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

Expand \left(3xy^{4}\right)^{2}.

$$\frac{4x^{6}y^{2}\times 3^{2}x^{2}\left(y^{4}\right)^{2}}{\left(5xy^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{4x^{6}y^{2}\times 3^{2}x^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{4x^{6}y^{2}\times 9x^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

Multiply 4 and 9 to get 36.

$$\frac{36x^{6}y^{2}x^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

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

$$\frac{36x^{8}y^{2}y^{8}}{\left(5xy^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{36x^{8}y^{10}}{\left(5xy^{2}\right)^{2}}$$

Expand \left(5xy^{2}\right)^{2}.

$$\frac{36x^{8}y^{10}}{5^{2}x^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{36x^{8}y^{10}}{5^{2}x^{2}y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{36x^{8}y^{10}}{25x^{2}y^{4}}$$

Cancel out x^{2}y^{4} in both numerator and denominator.

$$\frac{36x^{6}y^{6}}{25}$$