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

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

Evaluate

$$-108x^{7}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 3 and get 27.

$$\left(-4x^{4}\right)\times 27x^{3}$$

Multiply -1 and 4 to get -4.

$$-4x^{4}\times 27x^{3}$$

Multiply -4 and 27 to get -108.

$$-108x^{4}x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-108x^{7}$$

Expand

$$-108x^{7}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 3 to the power of 3 and get 27.

$$\left(-4x^{4}\right)\times 27x^{3}$$

Multiply -1 and 4 to get -4.

$$-4x^{4}\times 27x^{3}$$

Multiply -4 and 27 to get -108.

$$-108x^{4}x^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$-108x^{7}$$