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

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

Evaluate

$$\frac{1}{y^{18}x^{21}}$$

Solution Steps

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

$$\left(\frac{x^{-3}}{x^{4}y^{6}}\right)^{3}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{y^{6}x^{7}}\right)^{3}$$

To raise \frac{1}{y^{6}x^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(y^{6}x^{7}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(y^{6}x^{7}\right)^{3}}$$

Expand \left(y^{6}x^{7}\right)^{3}.

$$\frac{1}{\left(y^{6}\right)^{3}\left(x^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{1}{y^{18}\left(x^{7}\right)^{3}}$$

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

$$\frac{1}{y^{18}x^{21}}$$

Expand

$$\frac{1}{y^{18}x^{21}}$$

Solution Steps

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

$$\left(\frac{x^{-3}}{x^{4}y^{6}}\right)^{3}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{y^{6}x^{7}}\right)^{3}$$

To raise \frac{1}{y^{6}x^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(y^{6}x^{7}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(y^{6}x^{7}\right)^{3}}$$

Expand \left(y^{6}x^{7}\right)^{3}.

$$\frac{1}{\left(y^{6}\right)^{3}\left(x^{7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{1}{y^{18}\left(x^{7}\right)^{3}}$$

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

$$\frac{1}{y^{18}x^{21}}$$