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

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

Evaluate

$$8x^{6}+9a^{6}$$

Solution Steps

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$9a^{6}-\left(-2x^{2}\right)^{3}$$

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

$$9a^{6}-\left(-2\right)^{3}\left(x^{2}\right)^{3}$$

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

$$9a^{6}-\left(-2\right)^{3}x^{6}$$

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

$$9a^{6}-\left(-8x^{6}\right)$$

The opposite of -8x^{6} is 8x^{6}.

$$9a^{6}+8x^{6}$$

Expand

$$8x^{6}+9a^{6}$$

Solution Steps

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

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

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

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

Calculate -3 to the power of 2 and get 9.

$$9a^{6}-\left(-2x^{2}\right)^{3}$$

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

$$9a^{6}-\left(-2\right)^{3}\left(x^{2}\right)^{3}$$

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

$$9a^{6}-\left(-2\right)^{3}x^{6}$$

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

$$9a^{6}-\left(-8x^{6}\right)$$

The opposite of -8x^{6} is 8x^{6}.

$$9a^{6}+8x^{6}$$