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

$$( 3 x ) ^ { 3 } \times ( 2 x ) ^ { 3 } \times ( - 3 x ^ { 2 } ) ^ { 3 }$$

Evaluate

$$-5832x^{12}$$

Solution Steps

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

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

Calculate 3 to the power of 3 and get 27.

$$27x^{3}\times \left(2x\right)^{3}\left(-3x^{2}\right)^{3}$$

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

$$27x^{3}\times 2^{3}x^{3}\left(-3x^{2}\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$27x^{3}\times 8x^{3}\left(-3x^{2}\right)^{3}$$

Multiply 27 and 8 to get 216.

$$216x^{3}x^{3}\left(-3x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$216x^{6}\left(-3x^{2}\right)^{3}$$

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

$$216x^{6}\left(-3\right)^{3}\left(x^{2}\right)^{3}$$

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

$$216x^{6}\left(-3\right)^{3}x^{6}$$

Calculate -3 to the power of 3 and get -27.

$$216x^{6}\left(-27\right)x^{6}$$

Multiply 216 and -27 to get -5832.

$$-5832x^{6}x^{6}$$

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

$$-5832x^{12}$$

Expand

$$-5832x^{12}$$

Solution Steps

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

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

Calculate 3 to the power of 3 and get 27.

$$27x^{3}\times \left(2x\right)^{3}\left(-3x^{2}\right)^{3}$$

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

$$27x^{3}\times 2^{3}x^{3}\left(-3x^{2}\right)^{3}$$

Calculate 2 to the power of 3 and get 8.

$$27x^{3}\times 8x^{3}\left(-3x^{2}\right)^{3}$$

Multiply 27 and 8 to get 216.

$$216x^{3}x^{3}\left(-3x^{2}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$216x^{6}\left(-3x^{2}\right)^{3}$$

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

$$216x^{6}\left(-3\right)^{3}\left(x^{2}\right)^{3}$$

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

$$216x^{6}\left(-3\right)^{3}x^{6}$$

Calculate -3 to the power of 3 and get -27.

$$216x^{6}\left(-27\right)x^{6}$$

Multiply 216 and -27 to get -5832.

$$-5832x^{6}x^{6}$$

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

$$-5832x^{12}$$