Solve (-1/2a^3bz)^3

$$( - \frac { 1 } { 2 } a ^ { 3 } b z ) ^ { 3 }$$

Evaluate

$$-\frac{a^{9}\left(bz\right)^{3}}{8}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}a^{3}b^{1}z^{1}\right)^{3}$$

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

$$\left(-\frac{1}{2}\right)^{3}\left(a^{3}\right)^{3}\left(b^{1}\right)^{3}\left(z^{1}\right)^{3}$$

Raise -\frac{1}{2} to the power 3.

$$-\frac{1}{8}\left(a^{3}\right)^{3}\left(b^{1}\right)^{3}\left(z^{1}\right)^{3}$$

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

$$-\frac{1}{8}a^{3\times 3}b^{3}z^{3}$$

Multiply 3 times 3.

$$-\frac{1}{8}a^{9}b^{3}z^{3}$$

Expand

$$-\frac{a^{9}\left(bz\right)^{3}}{8}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}a^{3}b^{1}z^{1}\right)^{3}$$

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

$$\left(-\frac{1}{2}\right)^{3}\left(a^{3}\right)^{3}\left(b^{1}\right)^{3}\left(z^{1}\right)^{3}$$

Raise -\frac{1}{2} to the power 3.

$$-\frac{1}{8}\left(a^{3}\right)^{3}\left(b^{1}\right)^{3}\left(z^{1}\right)^{3}$$

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

$$-\frac{1}{8}a^{3\times 3}b^{3}z^{3}$$

Multiply 3 times 3.

$$-\frac{1}{8}a^{9}b^{3}z^{3}$$