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

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

Evaluate

$$-2048x^{17}y^{24}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-2\right)^{3}x^{9}\left(y^{4}\right)^{3}\left(-4x^{2}y^{3}\right)^{4}$$

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

$$\left(-2\right)^{3}x^{9}y^{12}\left(-4x^{2}y^{3}\right)^{4}$$

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

$$-8x^{9}y^{12}\left(-4x^{2}y^{3}\right)^{4}$$

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

$$-8x^{9}y^{12}\left(-4\right)^{4}\left(x^{2}\right)^{4}\left(y^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$-8x^{9}y^{12}\left(-4\right)^{4}x^{8}\left(y^{3}\right)^{4}$$

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

$$-8x^{9}y^{12}\left(-4\right)^{4}x^{8}y^{12}$$

Calculate -4 to the power of 4 and get 256.

$$-8x^{9}y^{12}\times 256x^{8}y^{12}$$

Multiply -8 and 256 to get -2048.

$$-2048x^{9}y^{12}x^{8}y^{12}$$

To multiply powers of the same base, add their exponents. Add 9 and 8 to get 17.

$$-2048x^{17}y^{12}y^{12}$$

To multiply powers of the same base, add their exponents. Add 12 and 12 to get 24.

$$-2048x^{17}y^{24}$$

Expand

$$-2048x^{17}y^{24}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(-2\right)^{3}x^{9}\left(y^{4}\right)^{3}\left(-4x^{2}y^{3}\right)^{4}$$

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

$$\left(-2\right)^{3}x^{9}y^{12}\left(-4x^{2}y^{3}\right)^{4}$$

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

$$-8x^{9}y^{12}\left(-4x^{2}y^{3}\right)^{4}$$

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

$$-8x^{9}y^{12}\left(-4\right)^{4}\left(x^{2}\right)^{4}\left(y^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$-8x^{9}y^{12}\left(-4\right)^{4}x^{8}\left(y^{3}\right)^{4}$$

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

$$-8x^{9}y^{12}\left(-4\right)^{4}x^{8}y^{12}$$

Calculate -4 to the power of 4 and get 256.

$$-8x^{9}y^{12}\times 256x^{8}y^{12}$$

Multiply -8 and 256 to get -2048.

$$-2048x^{9}y^{12}x^{8}y^{12}$$

To multiply powers of the same base, add their exponents. Add 9 and 8 to get 17.

$$-2048x^{17}y^{12}y^{12}$$

To multiply powers of the same base, add their exponents. Add 12 and 12 to get 24.

$$-2048x^{17}y^{24}$$