Solve (frac{2x^{2}y^3}{4x^9y^3})^3

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

Evaluate

$$\frac{1}{8x^{21}}$$

Solution Steps

Cancel out 2x^{2}y^{3} in both numerator and denominator.

$$\left(\frac{1}{2x^{7}}\right)^{3}$$

To raise \frac{1}{2x^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(2x^{7}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(2x^{7}\right)^{3}}$$

Expand \left(2x^{7}\right)^{3}.

$$\frac{1}{2^{3}\left(x^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{1}{2^{3}x^{21}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{8x^{21}}$$

Expand

$$\frac{1}{8x^{21}}$$

Solution Steps

Cancel out 2x^{2}y^{3} in both numerator and denominator.

$$\left(\frac{1}{2x^{7}}\right)^{3}$$

To raise \frac{1}{2x^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(2x^{7}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(2x^{7}\right)^{3}}$$

Expand \left(2x^{7}\right)^{3}.

$$\frac{1}{2^{3}\left(x^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{1}{2^{3}x^{21}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1}{8x^{21}}$$