Solve (3/2x)^3*4*x^4/9

$$( \frac { 3 } { 2 x } ) ^ { 3 } \cdot \frac { 4 \cdot x ^ { 4 } } { 9 }$$

Evaluate

$$\frac{3x}{2}$$

Solution Steps

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

$$\frac{3^{3}}{\left(2x\right)^{3}}\times \frac{4x^{4}}{9}$$

Multiply \frac{3^{3}}{\left(2x\right)^{3}} times \frac{4x^{4}}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3^{3}\times 4x^{4}}{\left(2x\right)^{3}\times 9}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27\times 4x^{4}}{\left(2x\right)^{3}\times 9}$$

Multiply 27 and 4 to get 108.

$$\frac{108x^{4}}{\left(2x\right)^{3}\times 9}$$

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

$$\frac{108x^{4}}{2^{3}x^{3}\times 9}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{108x^{4}}{8x^{3}\times 9}$$

Multiply 8 and 9 to get 72.

$$\frac{108x^{4}}{72x^{3}}$$

Cancel out 36x^{3} in both numerator and denominator.

$$\frac{3x}{2}$$

Expand

$$\frac{3x}{2}$$

Solution Steps

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

$$\frac{3^{3}}{\left(2x\right)^{3}}\times \frac{4x^{4}}{9}$$

Multiply \frac{3^{3}}{\left(2x\right)^{3}} times \frac{4x^{4}}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3^{3}\times 4x^{4}}{\left(2x\right)^{3}\times 9}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27\times 4x^{4}}{\left(2x\right)^{3}\times 9}$$

Multiply 27 and 4 to get 108.

$$\frac{108x^{4}}{\left(2x\right)^{3}\times 9}$$

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

$$\frac{108x^{4}}{2^{3}x^{3}\times 9}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{108x^{4}}{8x^{3}\times 9}$$

Multiply 8 and 9 to get 72.

$$\frac{108x^{4}}{72x^{3}}$$

Cancel out 36x^{3} in both numerator and denominator.

$$\frac{3x}{2}$$