Solve (-2xyz^3)^4(2y^2z^3)

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

Evaluate

$$32x^{4}y^{6}z^{15}$$

Solution Steps

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

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

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

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

Calculate -2 to the power of 4 and get 16.

$$16x^{4}y^{4}z^{12}\times 2y^{2}z^{3}$$

Multiply 16 and 2 to get 32.

$$32x^{4}y^{4}z^{12}y^{2}z^{3}$$

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

$$32x^{4}y^{6}z^{12}z^{3}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$32x^{4}y^{6}z^{15}$$

Expand

$$32x^{4}y^{6}z^{15}$$

Solution Steps

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

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

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

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

Calculate -2 to the power of 4 and get 16.

$$16x^{4}y^{4}z^{12}\times 2y^{2}z^{3}$$

Multiply 16 and 2 to get 32.

$$32x^{4}y^{4}z^{12}y^{2}z^{3}$$

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

$$32x^{4}y^{6}z^{12}z^{3}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$32x^{4}y^{6}z^{15}$$