Solve (4w^5/x^-6)^-3

$$( \frac { 4 w ^ { 5 } } { x ^ { - 6 } } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{64w^{15}x^{18}}$$

Solution Steps

To raise \frac{4w^{5}}{x^{-6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4w^{5}\right)^{-3}}{\left(x^{-6}\right)^{-3}}$$

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

$$\frac{\left(4w^{5}\right)^{-3}}{x^{18}}$$

Expand \left(4w^{5}\right)^{-3}.

$$\frac{4^{-3}\left(w^{5}\right)^{-3}}{x^{18}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{4^{-3}w^{-15}}{x^{18}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{64}w^{-15}}{x^{18}}$$

Expand

$$\frac{1}{64w^{15}x^{18}}$$

Solution Steps

To raise \frac{4w^{5}}{x^{-6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4w^{5}\right)^{-3}}{\left(x^{-6}\right)^{-3}}$$

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

$$\frac{\left(4w^{5}\right)^{-3}}{x^{18}}$$

Expand \left(4w^{5}\right)^{-3}.

$$\frac{4^{-3}\left(w^{5}\right)^{-3}}{x^{18}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{4^{-3}w^{-15}}{x^{18}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{64}w^{-15}}{x^{18}}$$