Solve frac{(48x^{7}y^{2})^3}{(36x^2y^2)^2}

$$\frac { ( 48 x ^ { 7 } y ^ { 2 } ) ^ { 3 } } { ( 36 x ^ { 2 } y ^ { 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{256y^{2}x^{17}}{3}$$

Solution Steps

Expand \left(48x^{7}y^{2}\right)^{3}.

$$\frac{48^{3}\left(x^{7}\right)^{3}\left(y^{2}\right)^{3}}{\left(36x^{2}y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{48^{3}x^{21}\left(y^{2}\right)^{3}}{\left(36x^{2}y^{2}\right)^{2}}$$

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

$$\frac{48^{3}x^{21}y^{6}}{\left(36x^{2}y^{2}\right)^{2}}$$

Calculate 48 to the power of 3 and get 110592.

$$\frac{110592x^{21}y^{6}}{\left(36x^{2}y^{2}\right)^{2}}$$

Expand \left(36x^{2}y^{2}\right)^{2}.

$$\frac{110592x^{21}y^{6}}{36^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{110592x^{21}y^{6}}{36^{2}x^{4}\left(y^{2}\right)^{2}}$$

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

$$\frac{110592x^{21}y^{6}}{36^{2}x^{4}y^{4}}$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{110592x^{21}y^{6}}{1296x^{4}y^{4}}$$

Cancel out 432x^{4}y^{4} in both numerator and denominator.

$$\frac{256y^{2}x^{17}}{3}$$

Expand

$$\frac{256y^{2}x^{17}}{3}$$

Solution Steps

Expand \left(48x^{7}y^{2}\right)^{3}.

$$\frac{48^{3}\left(x^{7}\right)^{3}\left(y^{2}\right)^{3}}{\left(36x^{2}y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{48^{3}x^{21}\left(y^{2}\right)^{3}}{\left(36x^{2}y^{2}\right)^{2}}$$

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

$$\frac{48^{3}x^{21}y^{6}}{\left(36x^{2}y^{2}\right)^{2}}$$

Calculate 48 to the power of 3 and get 110592.

$$\frac{110592x^{21}y^{6}}{\left(36x^{2}y^{2}\right)^{2}}$$

Expand \left(36x^{2}y^{2}\right)^{2}.

$$\frac{110592x^{21}y^{6}}{36^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}}$$

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

$$\frac{110592x^{21}y^{6}}{36^{2}x^{4}\left(y^{2}\right)^{2}}$$

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

$$\frac{110592x^{21}y^{6}}{36^{2}x^{4}y^{4}}$$

Calculate 36 to the power of 2 and get 1296.

$$\frac{110592x^{21}y^{6}}{1296x^{4}y^{4}}$$

Cancel out 432x^{4}y^{4} in both numerator and denominator.

$$\frac{256y^{2}x^{17}}{3}$$