Solve (-1/2xy^3z^3)^4

$$( - \frac { 1 } { 2 } x y ^ { 3 } z ^ { 3 } ) ^ { 4 }$$

Evaluate

$$\frac{x^{4}\left(yz\right)^{12}}{16}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}x^{1}y^{3}z^{3}\right)^{4}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{1}{2}\right)^{4}\left(x^{1}\right)^{4}\left(y^{3}\right)^{4}\left(z^{3}\right)^{4}$$

Raise -\frac{1}{2} to the power 4.

$$\frac{1}{16}\left(x^{1}\right)^{4}\left(y^{3}\right)^{4}\left(z^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{16}x^{4}y^{3\times 4}z^{3\times 4}$$

Multiply 3 times 4.

$$\frac{1}{16}x^{4}y^{12}z^{3\times 4}$$

Multiply 3 times 4.

$$\frac{1}{16}x^{4}y^{12}z^{12}$$

Expand

$$\frac{x^{4}\left(yz\right)^{12}}{16}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}x^{1}y^{3}z^{3}\right)^{4}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-\frac{1}{2}\right)^{4}\left(x^{1}\right)^{4}\left(y^{3}\right)^{4}\left(z^{3}\right)^{4}$$

Raise -\frac{1}{2} to the power 4.

$$\frac{1}{16}\left(x^{1}\right)^{4}\left(y^{3}\right)^{4}\left(z^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{16}x^{4}y^{3\times 4}z^{3\times 4}$$

Multiply 3 times 4.

$$\frac{1}{16}x^{4}y^{12}z^{3\times 4}$$

Multiply 3 times 4.

$$\frac{1}{16}x^{4}y^{12}z^{12}$$