Solve (4x^3y)^4/(4xy^2)^3

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

Evaluate

$$\frac{4x^{9}}{y^{2}}$$

Solution Steps

Expand \left(4x^{3}y\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{4^{4}x^{12}y^{4}}{\left(4xy^{2}\right)^{3}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{256x^{12}y^{4}}{\left(4xy^{2}\right)^{3}}$$

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

$$\frac{256x^{12}y^{4}}{4^{3}x^{3}\left(y^{2}\right)^{3}}$$

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

$$\frac{256x^{12}y^{4}}{4^{3}x^{3}y^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{256x^{12}y^{4}}{64x^{3}y^{6}}$$

Cancel out 64x^{3}y^{4} in both numerator and denominator.

$$\frac{4x^{9}}{y^{2}}$$

Expand

$$\frac{4x^{9}}{y^{2}}$$

Solution Steps

Expand \left(4x^{3}y\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{4^{4}x^{12}y^{4}}{\left(4xy^{2}\right)^{3}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{256x^{12}y^{4}}{\left(4xy^{2}\right)^{3}}$$

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

$$\frac{256x^{12}y^{4}}{4^{3}x^{3}\left(y^{2}\right)^{3}}$$

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

$$\frac{256x^{12}y^{4}}{4^{3}x^{3}y^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{256x^{12}y^{4}}{64x^{3}y^{6}}$$

Cancel out 64x^{3}y^{4} in both numerator and denominator.

$$\frac{4x^{9}}{y^{2}}$$