Solve (-3a^2b^5c^3)^3

$$( - 3 a ^ { 2 } b ^ { 5 } c ^ { 3 } ) ^ { 3 }$$

Evaluate

$$-27a^{6}c^{9}b^{15}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-3a^{2}b^{5}c^{3}\right)^{3}$$

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}\left(b^{5}\right)^{3}\left(c^{3}\right)^{3}$$

Raise -3 to the power 3.

$$-27\left(a^{2}\right)^{3}\left(b^{5}\right)^{3}\left(c^{3}\right)^{3}$$

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

$$-27a^{2\times 3}b^{5\times 3}c^{3\times 3}$$

Multiply 2 times 3.

$$-27a^{6}b^{5\times 3}c^{3\times 3}$$

Multiply 5 times 3.

$$-27a^{6}b^{15}c^{3\times 3}$$

Multiply 3 times 3.

$$-27a^{6}b^{15}c^{9}$$

Expand

$$-27a^{6}c^{9}b^{15}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(-3a^{2}b^{5}c^{3}\right)^{3}$$

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

$$\left(-3\right)^{3}\left(a^{2}\right)^{3}\left(b^{5}\right)^{3}\left(c^{3}\right)^{3}$$

Raise -3 to the power 3.

$$-27\left(a^{2}\right)^{3}\left(b^{5}\right)^{3}\left(c^{3}\right)^{3}$$

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

$$-27a^{2\times 3}b^{5\times 3}c^{3\times 3}$$

Multiply 2 times 3.

$$-27a^{6}b^{5\times 3}c^{3\times 3}$$

Multiply 5 times 3.

$$-27a^{6}b^{15}c^{3\times 3}$$

Multiply 3 times 3.

$$-27a^{6}b^{15}c^{9}$$