Solve (4x^5y)^3/(2x^7y)^2

$$\frac { ( 4 x ^ { 5 } y ) ^ { 3 } } { ( 2 x ^ { 7 } y ) ^ { 2 } }$$

Evaluate

$$16xy$$

Solution Steps

Expand \left(4x^{5}y\right)^{3}.

$$\frac{4^{3}\left(x^{5}\right)^{3}y^{3}}{\left(2x^{7}y\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{4^{3}x^{15}y^{3}}{\left(2x^{7}y\right)^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{15}y^{3}}{\left(2x^{7}y\right)^{2}}$$

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

$$\frac{64x^{15}y^{3}}{2^{2}\left(x^{7}\right)^{2}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{64x^{15}y^{3}}{2^{2}x^{14}y^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{64x^{15}y^{3}}{4x^{14}y^{2}}$$

Cancel out 4y^{2}x^{14} in both numerator and denominator.

$$16xy$$

Expand

$$16xy$$

Solution Steps

Expand \left(4x^{5}y\right)^{3}.

$$\frac{4^{3}\left(x^{5}\right)^{3}y^{3}}{\left(2x^{7}y\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{4^{3}x^{15}y^{3}}{\left(2x^{7}y\right)^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{15}y^{3}}{\left(2x^{7}y\right)^{2}}$$

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

$$\frac{64x^{15}y^{3}}{2^{2}\left(x^{7}\right)^{2}y^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{64x^{15}y^{3}}{2^{2}x^{14}y^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{64x^{15}y^{3}}{4x^{14}y^{2}}$$

Cancel out 4y^{2}x^{14} in both numerator and denominator.

$$16xy$$