Solve (-4a^3b^3c^2)^3

$$( - 4 a ^ { 3 } b ^ { 3 } c ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-64c^{6}\left(ab\right)^{9}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-4a^{3}b^{3}c^{2}\right)^{3}$$

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

$$\left(-4\right)^{3}\left(a^{3}\right)^{3}\left(b^{3}\right)^{3}\left(c^{2}\right)^{3}$$

Raise -4 to the power 3.

$$-64\left(a^{3}\right)^{3}\left(b^{3}\right)^{3}\left(c^{2}\right)^{3}$$

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

$$-64a^{3\times 3}b^{3\times 3}c^{2\times 3}$$

Multiply 3 times 3.

$$-64a^{9}b^{3\times 3}c^{2\times 3}$$

Multiply 3 times 3.

$$-64a^{9}b^{9}c^{2\times 3}$$

Multiply 2 times 3.

$$-64a^{9}b^{9}c^{6}$$

Expand

$$-64c^{6}\left(ab\right)^{9}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-4a^{3}b^{3}c^{2}\right)^{3}$$

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

$$\left(-4\right)^{3}\left(a^{3}\right)^{3}\left(b^{3}\right)^{3}\left(c^{2}\right)^{3}$$

Raise -4 to the power 3.

$$-64\left(a^{3}\right)^{3}\left(b^{3}\right)^{3}\left(c^{2}\right)^{3}$$

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

$$-64a^{3\times 3}b^{3\times 3}c^{2\times 3}$$

Multiply 3 times 3.

$$-64a^{9}b^{3\times 3}c^{2\times 3}$$

Multiply 3 times 3.

$$-64a^{9}b^{9}c^{2\times 3}$$

Multiply 2 times 3.

$$-64a^{9}b^{9}c^{6}$$