Solve (3)[(x^2)^3*(-x)^3]^2

$$( 3 ) [ ( x ^ { 2 } ) ^ { 3 } \cdot ( - x ) ^ { 3 } ] ^ { 2 }$$

Evaluate

$$3x^{18}$$

Solution Steps

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

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

Expand \left(x^{6}\left(-x\right)^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$3x^{12}\left(\left(-x\right)^{3}\right)^{2}$$

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

$$3x^{12}\left(-x\right)^{6}$$

Expand \left(-x\right)^{6}.

$$3x^{12}\left(-1\right)^{6}x^{6}$$

Calculate -1 to the power of 6 and get 1.

$$3x^{12}\times 1x^{6}$$

Multiply 3 and 1 to get 3.

$$3x^{12}x^{6}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$3x^{18}$$

Expand

$$3x^{18}$$

Solution Steps

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

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

Expand \left(x^{6}\left(-x\right)^{3}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$3x^{12}\left(\left(-x\right)^{3}\right)^{2}$$

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

$$3x^{12}\left(-x\right)^{6}$$

Expand \left(-x\right)^{6}.

$$3x^{12}\left(-1\right)^{6}x^{6}$$

Calculate -1 to the power of 6 and get 1.

$$3x^{12}\times 1x^{6}$$

Multiply 3 and 1 to get 3.

$$3x^{12}x^{6}$$

To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.

$$3x^{18}$$