Solve (-3x^{3})^{2}-[-(2x)^2]^3-3x^4(-x)^2=

$$( - 3 x ^ { 3 } ) ^ { 2 } - [ - ( 2 x ) ^ { 2 } ] ^ { 3 } - 3 x ^ { 4 } ( - x ) ^ { 2 } =$$

Evaluate

$$70x^{6}$$

Solution Steps

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

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

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

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

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

$$9x^{6}-\left(-\left(2x\right)^{2}\right)^{3}-3x^{4}\left(-x\right)^{2}$$

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

$$9x^{6}-\left(-2^{2}x^{2}\right)^{3}-3x^{4}\left(-x\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$9x^{6}-\left(-4x^{2}\right)^{3}-3x^{4}\left(-x\right)^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$9x^{6}-\left(-4x^{2}\right)^{3}-3x^{4}x^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$9x^{6}-\left(-4x^{2}\right)^{3}-3x^{6}$$

Expand \left(-4x^{2}\right)^{3}.

$$9x^{6}-\left(-4\right)^{3}\left(x^{2}\right)^{3}-3x^{6}$$

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

$$9x^{6}-\left(-4\right)^{3}x^{6}-3x^{6}$$

Calculate -4 to the power of 3 and get -64.

$$9x^{6}-\left(-64x^{6}\right)-3x^{6}$$

Multiply -1 and -64 to get 64.

$$9x^{6}+64x^{6}-3x^{6}$$

Combine 9x^{6} and 64x^{6} to get 73x^{6}.

$$73x^{6}-3x^{6}$$

Combine 73x^{6} and -3x^{6} to get 70x^{6}.

$$70x^{6}$$

Expand

$$70x^{6}$$

Solution Steps

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

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

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

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

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

$$9x^{6}-\left(-\left(2x\right)^{2}\right)^{3}-3x^{4}\left(-x\right)^{2}$$

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

$$9x^{6}-\left(-2^{2}x^{2}\right)^{3}-3x^{4}\left(-x\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$9x^{6}-\left(-4x^{2}\right)^{3}-3x^{4}\left(-x\right)^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$9x^{6}-\left(-4x^{2}\right)^{3}-3x^{4}x^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$9x^{6}-\left(-4x^{2}\right)^{3}-3x^{6}$$

Expand \left(-4x^{2}\right)^{3}.

$$9x^{6}-\left(-4\right)^{3}\left(x^{2}\right)^{3}-3x^{6}$$

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

$$9x^{6}-\left(-4\right)^{3}x^{6}-3x^{6}$$

Calculate -4 to the power of 3 and get -64.

$$9x^{6}-\left(-64x^{6}\right)-3x^{6}$$

Multiply -1 and -64 to get 64.

$$9x^{6}+64x^{6}-3x^{6}$$

Combine 9x^{6} and 64x^{6} to get 73x^{6}.

$$73x^{6}-3x^{6}$$

Combine 73x^{6} and -3x^{6} to get 70x^{6}.

$$70x^{6}$$