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

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

Evaluate

$$12\left(ab\right)^{6}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Calculate -2 to the power of 2 and get 4.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Calculate -2 to the power of 3 and get -8.

$$4a^{6}b^{6}-\left(-8a^{6}b^{6}\right)$$

The opposite of -8a^{6}b^{6} is 8a^{6}b^{6}.

$$4a^{6}b^{6}+8a^{6}b^{6}$$

Combine 4a^{6}b^{6} and 8a^{6}b^{6} to get 12a^{6}b^{6}.

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

Expand

$$12\left(ab\right)^{6}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

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

Calculate -2 to the power of 2 and get 4.

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

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Calculate -2 to the power of 3 and get -8.

$$4a^{6}b^{6}-\left(-8a^{6}b^{6}\right)$$

The opposite of -8a^{6}b^{6} is 8a^{6}b^{6}.

$$4a^{6}b^{6}+8a^{6}b^{6}$$

Combine 4a^{6}b^{6} and 8a^{6}b^{6} to get 12a^{6}b^{6}.

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