Solve (5xy^3/x^5y)^-3

$$( \frac { 5 x y ^ { 3 } } { x ^ { 5 } y } ) ^ { - 3 }$$

Evaluate

$$\frac{x^{12}}{125y^{6}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

$$\left(\frac{5y^{2}}{x^{4}}\right)^{-3}$$

To raise \frac{5y^{2}}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5y^{2}\right)^{-3}}{\left(x^{4}\right)^{-3}}$$

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

$$\frac{\left(5y^{2}\right)^{-3}}{x^{-12}}$$

Expand \left(5y^{2}\right)^{-3}.

$$\frac{5^{-3}\left(y^{2}\right)^{-3}}{x^{-12}}$$

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

$$\frac{5^{-3}y^{-6}}{x^{-12}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{125}y^{-6}}{x^{-12}}$$

Expand

$$\frac{x^{12}}{125y^{6}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

$$\left(\frac{5y^{2}}{x^{4}}\right)^{-3}$$

To raise \frac{5y^{2}}{x^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5y^{2}\right)^{-3}}{\left(x^{4}\right)^{-3}}$$

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

$$\frac{\left(5y^{2}\right)^{-3}}{x^{-12}}$$

Expand \left(5y^{2}\right)^{-3}.

$$\frac{5^{-3}\left(y^{2}\right)^{-3}}{x^{-12}}$$

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

$$\frac{5^{-3}y^{-6}}{x^{-12}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{1}{125}y^{-6}}{x^{-12}}$$