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

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

Evaluate

$$\frac{12}{x^{5}}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

$$\frac{12x^{4}}{x^{9}}$$

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

$$\frac{12}{x^{5}}$$

Expand

$$\frac{12}{x^{5}}$$

Solution Steps

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

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

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

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

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

$$\frac{12x^{4}}{x^{9}}$$

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

$$\frac{12}{x^{5}}$$