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

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

Evaluate

$$\frac{9}{16x^{4}}$$

Solution Steps

Cancel out x in both numerator and denominator.

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

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

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

Express \frac{\frac{3}{4}}{x^{2}} as a single fraction.

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

To raise \frac{3}{4x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{\left(4x^{2}\right)^{2}}$$

Expand \left(4x^{2}\right)^{2}.

$$\frac{9}{4^{2}\left(x^{2}\right)^{2}}$$

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

$$\frac{9}{4^{2}x^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9}{16x^{4}}$$

Expand

$$\frac{9}{16x^{4}}$$

Solution Steps

Cancel out x in both numerator and denominator.

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

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

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

Express \frac{\frac{3}{4}}{x^{2}} as a single fraction.

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

To raise \frac{3}{4x^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{\left(4x^{2}\right)^{2}}$$

Expand \left(4x^{2}\right)^{2}.

$$\frac{9}{4^{2}\left(x^{2}\right)^{2}}$$

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

$$\frac{9}{4^{2}x^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9}{16x^{4}}$$