Solve (-2x^2y)^3div4x^3y^2

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

Evaluate

$$-2y^{5}x^{9}$$

Solution Steps

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$\frac{-8x^{6}y^{3}}{4}x^{3}y^{2}$$

Divide -8x^{6}y^{3} by 4 to get -2x^{6}y^{3}.

$$-2x^{6}y^{3}x^{3}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-2x^{9}y^{3}y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-2x^{9}y^{5}$$

Expand

$$-2y^{5}x^{9}$$

Solution Steps

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$\frac{-8x^{6}y^{3}}{4}x^{3}y^{2}$$

Divide -8x^{6}y^{3} by 4 to get -2x^{6}y^{3}.

$$-2x^{6}y^{3}x^{3}y^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-2x^{9}y^{3}y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-2x^{9}y^{5}$$