Solve -2xy^{2}z^4*(-x^2yz^3)^4

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

Evaluate

$$-2y^{6}x^{9}z^{16}$$

Solution Steps

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$-2xy^{6}z^{16}\left(-x^{2}\right)^{4}$$

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

$$-2xy^{6}z^{16}\left(-1\right)^{4}\left(x^{2}\right)^{4}$$

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

$$-2xy^{6}z^{16}\left(-1\right)^{4}x^{8}$$

Calculate -1 to the power of 4 and get 1.

$$-2xy^{6}z^{16}x^{8}$$

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

$$-2x^{9}y^{6}z^{16}$$

Expand

$$-2y^{6}x^{9}z^{16}$$

Solution Steps

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 12 to get 16.

$$-2xy^{6}z^{16}\left(-x^{2}\right)^{4}$$

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

$$-2xy^{6}z^{16}\left(-1\right)^{4}\left(x^{2}\right)^{4}$$

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

$$-2xy^{6}z^{16}\left(-1\right)^{4}x^{8}$$

Calculate -1 to the power of 4 and get 1.

$$-2xy^{6}z^{16}x^{8}$$

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

$$-2x^{9}y^{6}z^{16}$$