Solve 1/3(x^2)^3/(frac{1{6}x^3)^2}

$$\frac { \frac { 1 } { 3 } ( x ^ { 2 } ) ^ { 3 } } { ( \frac { 1 } { 6 } x ^ { 3 } ) ^ { 2 } }$$

Evaluate

$$12$$

Solution Steps

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

$$\frac{\frac{1}{3}x^{6}}{\left(\frac{1}{6}x^{3}\right)^{2}}$$

Expand \left(\frac{1}{6}x^{3}\right)^{2}.

$$\frac{\frac{1}{3}x^{6}}{\left(\frac{1}{6}\right)^{2}\left(x^{3}\right)^{2}}$$

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

$$\frac{\frac{1}{3}x^{6}}{\left(\frac{1}{6}\right)^{2}x^{6}}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{\frac{1}{3}x^{6}}{\frac{1}{36}x^{6}}$$

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

$$\frac{\frac{1}{3}}{\frac{1}{36}}$$

Divide \frac{1}{3} by \frac{1}{36} by multiplying \frac{1}{3} by the reciprocal of \frac{1}{36}.

$$\frac{1}{3}\times 36$$

Multiply \frac{1}{3} and 36 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$