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

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

Evaluate

$$-27b^{6}a^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 3.

$$-27\left(a^{4}\right)^{3}\left(b^{2}\right)^{3}$$

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

$$-27a^{4\times 3}b^{2\times 3}$$

Multiply 4 times 3.

$$-27a^{12}b^{2\times 3}$$

Multiply 2 times 3.

$$-27a^{12}b^{6}$$

Expand

$$-27b^{6}a^{12}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise -3 to the power 3.

$$-27\left(a^{4}\right)^{3}\left(b^{2}\right)^{3}$$

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

$$-27a^{4\times 3}b^{2\times 3}$$

Multiply 4 times 3.

$$-27a^{12}b^{2\times 3}$$

Multiply 2 times 3.

$$-27a^{12}b^{6}$$