Solve (-2x^{4}y^{-2})^3(-y^3)(2x^3y)^2

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

Evaluate

$$\frac{32x^{18}}{y}$$

Solution Steps

Expand \left(-2x^{4}y^{-2}\right)^{3}.

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

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

$$\left(-2\right)^{3}x^{12}\left(y^{-2}\right)^{3}\left(-y^{3}\right)\times \left(2x^{3}y\right)^{2}$$

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

$$\left(-2\right)^{3}x^{12}y^{-6}\left(-y^{3}\right)\times \left(2x^{3}y\right)^{2}$$

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

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times \left(2x^{3}y\right)^{2}$$

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

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times 2^{2}\left(x^{3}\right)^{2}y^{2}$$

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

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times 2^{2}x^{6}y^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times 4x^{6}y^{2}$$

Multiply -8 and 4 to get -32.

$$-32x^{12}y^{-6}\left(-y^{3}\right)x^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$-32x^{18}y^{-6}\left(-y^{3}\right)y^{2}$$

To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.

$$-32x^{18}y^{-4}\left(-y^{3}\right)$$

Multiply -32 and -1 to get 32.

$$32x^{18}y^{-4}y^{3}$$

To multiply powers of the same base, add their exponents. Add -4 and 3 to get -1.

$$32x^{18}y^{-1}$$

Expand

$$\frac{32x^{18}}{y}$$

Solution Steps

Expand \left(-2x^{4}y^{-2}\right)^{3}.

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

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

$$\left(-2\right)^{3}x^{12}\left(y^{-2}\right)^{3}\left(-y^{3}\right)\times \left(2x^{3}y\right)^{2}$$

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

$$\left(-2\right)^{3}x^{12}y^{-6}\left(-y^{3}\right)\times \left(2x^{3}y\right)^{2}$$

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

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times \left(2x^{3}y\right)^{2}$$

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

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times 2^{2}\left(x^{3}\right)^{2}y^{2}$$

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

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times 2^{2}x^{6}y^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-8x^{12}y^{-6}\left(-y^{3}\right)\times 4x^{6}y^{2}$$

Multiply -8 and 4 to get -32.

$$-32x^{12}y^{-6}\left(-y^{3}\right)x^{6}y^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$-32x^{18}y^{-6}\left(-y^{3}\right)y^{2}$$

To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.

$$-32x^{18}y^{-4}\left(-y^{3}\right)$$

Multiply -32 and -1 to get 32.

$$32x^{18}y^{-4}y^{3}$$

To multiply powers of the same base, add their exponents. Add -4 and 3 to get -1.

$$32x^{18}y^{-1}$$