Solve (y^-1/5x^-1)^-3

$$( \frac { y ^ { - 1 } } { 5 x ^ { - 1 } } ) ^ { - 3 }$$

Evaluate

$$125\times \left(\frac{y}{x}\right)^{3}$$

Solution Steps

To raise \frac{y^{-1}}{5x^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{-1}\right)^{-3}}{\left(5x^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{y^{3}}{\left(5x^{-1}\right)^{-3}}$$

Expand \left(5x^{-1}\right)^{-3}.

$$\frac{y^{3}}{5^{-3}\left(x^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

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

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

$$\frac{y^{3}}{\frac{1}{125}x^{3}}$$

Expand

$$125\times \left(\frac{y}{x}\right)^{3}$$

Solution Steps

To raise \frac{y^{-1}}{5x^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(y^{-1}\right)^{-3}}{\left(5x^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{y^{3}}{\left(5x^{-1}\right)^{-3}}$$

Expand \left(5x^{-1}\right)^{-3}.

$$\frac{y^{3}}{5^{-3}\left(x^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

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

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

$$\frac{y^{3}}{\frac{1}{125}x^{3}}$$