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

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

Evaluate

$$-4x^{2}y^{14}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{3}x^{6}y^{15}}{-2x^{4}y}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{6}y^{15}}{-2x^{4}y}$$

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

$$\frac{4x^{2}y^{14}}{-1}$$

Anything divided by -1 gives its opposite.

$$-4x^{2}y^{14}$$

Expand

$$-4x^{2}y^{14}$$

Solution Steps

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

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

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

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

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

$$\frac{2^{3}x^{6}y^{15}}{-2x^{4}y}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{6}y^{15}}{-2x^{4}y}$$

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

$$\frac{4x^{2}y^{14}}{-1}$$

Anything divided by -1 gives its opposite.

$$-4x^{2}y^{14}$$