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

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

Evaluate

$$81y^{12}\left(mz\right)^{8}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 4.

$$81\left(y^{3}\right)^{4}\left(z^{2}\right)^{4}\left(m^{2}\right)^{4}$$

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

$$81y^{3\times 4}z^{2\times 4}m^{2\times 4}$$

Multiply 3 times 4.

$$81y^{12}z^{2\times 4}m^{2\times 4}$$

Multiply 2 times 4.

$$81y^{12}z^{8}m^{2\times 4}$$

Multiply 2 times 4.

$$81y^{12}z^{8}m^{8}$$

Expand

$$81y^{12}\left(mz\right)^{8}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 4.

$$81\left(y^{3}\right)^{4}\left(z^{2}\right)^{4}\left(m^{2}\right)^{4}$$

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

$$81y^{3\times 4}z^{2\times 4}m^{2\times 4}$$

Multiply 3 times 4.

$$81y^{12}z^{2\times 4}m^{2\times 4}$$

Multiply 2 times 4.

$$81y^{12}z^{8}m^{2\times 4}$$

Multiply 2 times 4.

$$81y^{12}z^{8}m^{8}$$