Solve frac{(2x^{3})^2(3x^4)}{(x^3)^4}

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

Evaluate

$$\frac{12}{x^{2}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(2x^{3}\right)^{2}\times 3x^{4}}{x^{12}}$$

Cancel out x^{4} in both numerator and denominator.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{3\times 4x^{6}}{x^{8}}$$

Multiply 3 and 4 to get 12.

$$\frac{12x^{6}}{x^{8}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{12}{x^{2}}$$

Expand

$$\frac{12}{x^{2}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\left(2x^{3}\right)^{2}\times 3x^{4}}{x^{12}}$$

Cancel out x^{4} in both numerator and denominator.

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{3\times 4x^{6}}{x^{8}}$$

Multiply 3 and 4 to get 12.

$$\frac{12x^{6}}{x^{8}}$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{12}{x^{2}}$$