Solve (-4a^2b^6)^3=

$$( - 4 a ^ { 2 } b ^ { 6 } ) ^ { 3 } =$$

Evaluate

$$-64a^{6}b^{18}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-4a^{2}b^{6}\right)^{3}$$

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

$$\left(-4\right)^{3}\left(a^{2}\right)^{3}\left(b^{6}\right)^{3}$$

Raise -4 to the power 3.

$$-64\left(a^{2}\right)^{3}\left(b^{6}\right)^{3}$$

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

$$-64a^{2\times 3}b^{6\times 3}$$

Multiply 2 times 3.

$$-64a^{6}b^{6\times 3}$$

Multiply 6 times 3.

$$-64a^{6}b^{18}$$

Expand

$$-64a^{6}b^{18}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-4a^{2}b^{6}\right)^{3}$$

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

$$\left(-4\right)^{3}\left(a^{2}\right)^{3}\left(b^{6}\right)^{3}$$

Raise -4 to the power 3.

$$-64\left(a^{2}\right)^{3}\left(b^{6}\right)^{3}$$

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

$$-64a^{2\times 3}b^{6\times 3}$$

Multiply 2 times 3.

$$-64a^{6}b^{6\times 3}$$

Multiply 6 times 3.

$$-64a^{6}b^{18}$$