Solve (2x^6/y^-4)^-3

$$( \frac { 2 x ^ { 6 } } { y ^ { - 4 } } ) ^ { - 3 }$$

Evaluate

$$\frac{1}{8y^{12}x^{18}}$$

Solution Steps

To raise \frac{2x^{6}}{y^{-4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{6}\right)^{-3}}{\left(y^{-4}\right)^{-3}}$$

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

$$\frac{\left(2x^{6}\right)^{-3}}{y^{12}}$$

Expand \left(2x^{6}\right)^{-3}.

$$\frac{2^{-3}\left(x^{6}\right)^{-3}}{y^{12}}$$

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

$$\frac{2^{-3}x^{-18}}{y^{12}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}x^{-18}}{y^{12}}$$

Expand

$$\frac{1}{8y^{12}x^{18}}$$

Solution Steps

To raise \frac{2x^{6}}{y^{-4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{6}\right)^{-3}}{\left(y^{-4}\right)^{-3}}$$

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

$$\frac{\left(2x^{6}\right)^{-3}}{y^{12}}$$

Expand \left(2x^{6}\right)^{-3}.

$$\frac{2^{-3}\left(x^{6}\right)^{-3}}{y^{12}}$$

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

$$\frac{2^{-3}x^{-18}}{y^{12}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{8}x^{-18}}{y^{12}}$$