Solve (-2/3a^2b^3c^2)^3

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

Evaluate

$$-\frac{8b^{9}\left(ac\right)^{6}}{27}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

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

$$-\frac{8}{27}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}\left(c^{2}\right)^{3}$$

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

$$-\frac{8}{27}a^{2\times 3}b^{3\times 3}c^{2\times 3}$$

Multiply 2 times 3.

$$-\frac{8}{27}a^{6}b^{3\times 3}c^{2\times 3}$$

Multiply 3 times 3.

$$-\frac{8}{27}a^{6}b^{9}c^{2\times 3}$$

Multiply 2 times 3.

$$-\frac{8}{27}a^{6}b^{9}c^{6}$$

Expand

$$-\frac{8b^{9}\left(ac\right)^{6}}{27}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

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

$$-\frac{8}{27}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}\left(c^{2}\right)^{3}$$

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

$$-\frac{8}{27}a^{2\times 3}b^{3\times 3}c^{2\times 3}$$

Multiply 2 times 3.

$$-\frac{8}{27}a^{6}b^{3\times 3}c^{2\times 3}$$

Multiply 3 times 3.

$$-\frac{8}{27}a^{6}b^{9}c^{2\times 3}$$

Multiply 2 times 3.

$$-\frac{8}{27}a^{6}b^{9}c^{6}$$