Solve {left(frac{x^2sqrt{3}}{2}right)}^2

$${ \left( \frac{ { x }^{ 2 } \sqrt{ 3 } }{ 2 } \right) }^{ 2 }$$

Evaluate

$$\frac{3x^{4}}{4}$$

Solution Steps

To raise \frac{x^{2}\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{2}\sqrt{3}\right)^{2}}{2^{2}}$$

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

$$\frac{\left(x^{2}\right)^{2}\left(\sqrt{3}\right)^{2}}{2^{2}}$$

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

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

The square of \sqrt{3} is 3.

$$\frac{x^{4}\times 3}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{4}\times 3}{4}$$

Expand

$$\frac{3x^{4}}{4}$$

Solution Steps

To raise \frac{x^{2}\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{2}\sqrt{3}\right)^{2}}{2^{2}}$$

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

$$\frac{\left(x^{2}\right)^{2}\left(\sqrt{3}\right)^{2}}{2^{2}}$$

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

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

The square of \sqrt{3} is 3.

$$\frac{x^{4}\times 3}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{4}\times 3}{4}$$