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

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

Evaluate

$$48x^{8}z^{9}y^{19}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(-2\right)^{4}x^{8}y^{16}\left(z^{2}\right)^{4}\times 3y^{3}z$$

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

$$\left(-2\right)^{4}x^{8}y^{16}z^{8}\times 3y^{3}z$$

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

$$16x^{8}y^{16}z^{8}\times 3y^{3}z$$

Multiply 16 and 3 to get 48.

$$48x^{8}y^{16}z^{8}y^{3}z$$

To multiply powers of the same base, add their exponents. Add 16 and 3 to get 19.

$$48x^{8}y^{19}z^{8}z$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$48x^{8}y^{19}z^{9}$$

Expand

$$48x^{8}z^{9}y^{19}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\left(-2\right)^{4}x^{8}y^{16}\left(z^{2}\right)^{4}\times 3y^{3}z$$

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

$$\left(-2\right)^{4}x^{8}y^{16}z^{8}\times 3y^{3}z$$

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

$$16x^{8}y^{16}z^{8}\times 3y^{3}z$$

Multiply 16 and 3 to get 48.

$$48x^{8}y^{16}z^{8}y^{3}z$$

To multiply powers of the same base, add their exponents. Add 16 and 3 to get 19.

$$48x^{8}y^{19}z^{8}z$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$48x^{8}y^{19}z^{9}$$