Solve (3y^3/z^-2)^-4

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

Evaluate

$$\frac{1}{81z^{8}y^{12}}$$

Solution Steps

To raise \frac{3y^{3}}{z^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -2 and -4 to get 8.

$$\frac{\left(3y^{3}\right)^{-4}}{z^{8}}$$

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

$$\frac{3^{-4}\left(y^{3}\right)^{-4}}{z^{8}}$$

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

$$\frac{3^{-4}y^{-12}}{z^{8}}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{\frac{1}{81}y^{-12}}{z^{8}}$$

Expand

$$\frac{1}{81z^{8}y^{12}}$$

Solution Steps

To raise \frac{3y^{3}}{z^{-2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply -2 and -4 to get 8.

$$\frac{\left(3y^{3}\right)^{-4}}{z^{8}}$$

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

$$\frac{3^{-4}\left(y^{3}\right)^{-4}}{z^{8}}$$

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

$$\frac{3^{-4}y^{-12}}{z^{8}}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{\frac{1}{81}y^{-12}}{z^{8}}$$