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

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

Evaluate

$$-128\left(xz\right)^{6}y^{24}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

$$-8x^{6}y^{12}z^{6}\times 2^{4}y^{12}$$

Calculate 2 to the power of 4 and get 16.

$$-8x^{6}y^{12}z^{6}\times 16y^{12}$$

Multiply -8 and 16 to get -128.

$$-128x^{6}y^{12}z^{6}y^{12}$$

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

$$-128x^{6}y^{24}z^{6}$$

Expand

$$-128\left(xz\right)^{6}y^{24}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

$$-8x^{6}y^{12}z^{6}\times 2^{4}y^{12}$$

Calculate 2 to the power of 4 and get 16.

$$-8x^{6}y^{12}z^{6}\times 16y^{12}$$

Multiply -8 and 16 to get -128.

$$-128x^{6}y^{12}z^{6}y^{12}$$

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

$$-128x^{6}y^{24}z^{6}$$