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

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

Evaluate

$$-8b^{6}a^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 3.

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

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

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

Multiply 3 times 3.

$$-8a^{9}b^{2\times 3}$$

Multiply 2 times 3.

$$-8a^{9}b^{6}$$

Expand

$$-8b^{6}a^{9}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -2 to the power 3.

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

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

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

Multiply 3 times 3.

$$-8a^{9}b^{2\times 3}$$

Multiply 2 times 3.

$$-8a^{9}b^{6}$$