Solve [1/4x*(-2x^2)^3]^2=

$$[ \frac { 1 } { 4 } x \cdot ( - 2 x ^ { 2 } ) ^ { 3 } ] ^ { 2 } =$$

Evaluate

$$4x^{14}$$

Solution Steps

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

$$\left(\frac{1}{4}x\left(-2\right)^{3}\left(x^{2}\right)^{3}\right)^{2}$$

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

$$\left(\frac{1}{4}x\left(-2\right)^{3}x^{6}\right)^{2}$$

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

$$\left(\frac{1}{4}x\left(-8\right)x^{6}\right)^{2}$$

Multiply \frac{1}{4} and -8 to get -2.

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

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\left(-2x^{7}\right)^{2}$$

Expand \left(-2x^{7}\right)^{2}.

$$\left(-2\right)^{2}\left(x^{7}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\left(-2\right)^{2}x^{14}$$

Calculate -2 to the power of 2 and get 4.

$$4x^{14}$$

Expand

$$4x^{14}$$

Solution Steps

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

$$\left(\frac{1}{4}x\left(-2\right)^{3}\left(x^{2}\right)^{3}\right)^{2}$$

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

$$\left(\frac{1}{4}x\left(-2\right)^{3}x^{6}\right)^{2}$$

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

$$\left(\frac{1}{4}x\left(-8\right)x^{6}\right)^{2}$$

Multiply \frac{1}{4} and -8 to get -2.

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

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\left(-2x^{7}\right)^{2}$$

Expand \left(-2x^{7}\right)^{2}.

$$\left(-2\right)^{2}\left(x^{7}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\left(-2\right)^{2}x^{14}$$

Calculate -2 to the power of 2 and get 4.

$$4x^{14}$$