Solve frac{(5x^{3}y^{2})^{2}}{4x^{2}y^6}divx^2/y^2x^4

$$\frac { ( 5 x ^ { 3 } y ^ { 2 } ) ^ { 2 } } { 4 x ^ { 2 } y ^ { 6 } } \div \frac { x ^ { 2 } } { y ^ { 2 } x ^ { 4 } }$$

Evaluate

$$\frac{25x^{6}}{4}$$

Solution Steps

Divide \frac{\left(5x^{3}y^{2}\right)^{2}}{4x^{2}y^{6}} by \frac{x^{2}}{y^{2}x^{4}} by multiplying \frac{\left(5x^{3}y^{2}\right)^{2}}{4x^{2}y^{6}} by the reciprocal of \frac{x^{2}}{y^{2}x^{4}}.

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

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

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

Expand \left(5y^{2}x^{3}\right)^{2}.

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

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

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

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

$$\frac{5^{2}y^{4}x^{6}}{4y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25y^{4}x^{6}}{4y^{4}}$$

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

$$\frac{25x^{6}}{4}$$

Expand

$$\frac{25x^{6}}{4}$$

Solution Steps

Divide \frac{\left(5x^{3}y^{2}\right)^{2}}{4x^{2}y^{6}} by \frac{x^{2}}{y^{2}x^{4}} by multiplying \frac{\left(5x^{3}y^{2}\right)^{2}}{4x^{2}y^{6}} by the reciprocal of \frac{x^{2}}{y^{2}x^{4}}.

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

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

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

Expand \left(5y^{2}x^{3}\right)^{2}.

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

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

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

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

$$\frac{5^{2}y^{4}x^{6}}{4y^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25y^{4}x^{6}}{4y^{4}}$$

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

$$\frac{25x^{6}}{4}$$