Solve (2x^2)^3*(3x)^2/2x^5

$$\frac { ( 2 x ^ { 2 } ) ^ { 3 } \times ( 3 x ) ^ { 2 } } { 2 x ^ { 5 } }$$

Evaluate

$$36x^{3}$$

Solution Steps

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

$$\frac{2^{3}\left(x^{2}\right)^{3}\times \left(3x\right)^{2}}{2x^{5}}$$

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

$$\frac{2^{3}x^{6}\times \left(3x\right)^{2}}{2x^{5}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{6}\times \left(3x\right)^{2}}{2x^{5}}$$

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

$$\frac{8x^{6}\times 3^{2}x^{2}}{2x^{5}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8x^{6}\times 9x^{2}}{2x^{5}}$$

Multiply 8 and 9 to get 72.

$$\frac{72x^{6}x^{2}}{2x^{5}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{72x^{8}}{2x^{5}}$$

Cancel out 2x^{5} in both numerator and denominator.

$$36x^{3}$$

Expand

$$36x^{3}$$

Solution Steps

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

$$\frac{2^{3}\left(x^{2}\right)^{3}\times \left(3x\right)^{2}}{2x^{5}}$$

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

$$\frac{2^{3}x^{6}\times \left(3x\right)^{2}}{2x^{5}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{6}\times \left(3x\right)^{2}}{2x^{5}}$$

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

$$\frac{8x^{6}\times 3^{2}x^{2}}{2x^{5}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8x^{6}\times 9x^{2}}{2x^{5}}$$

Multiply 8 and 9 to get 72.

$$\frac{72x^{6}x^{2}}{2x^{5}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{72x^{8}}{2x^{5}}$$

Cancel out 2x^{5} in both numerator and denominator.

$$36x^{3}$$