Solve (3z^2/4z^6)^-3

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

Evaluate

$$\frac{64z^{12}}{27}$$

Solution Steps

Cancel out z^{2} in both numerator and denominator.

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

To raise \frac{3}{4z^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{27}}{\left(4z^{4}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}}{4^{-3}\left(z^{4}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}}{4^{-3}z^{-12}}$$

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

$$\frac{\frac{1}{27}}{\frac{1}{64}z^{-12}}$$

Express \frac{\frac{1}{27}}{\frac{1}{64}z^{-12}} as a single fraction.

$$\frac{1}{27\times \frac{1}{64}z^{-12}}$$

Multiply 27 and \frac{1}{64} to get \frac{27}{64}.

$$\frac{1}{\frac{27}{64}z^{-12}}$$

Expand

$$\frac{64z^{12}}{27}$$

Solution Steps

Cancel out z^{2} in both numerator and denominator.

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

To raise \frac{3}{4z^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{27}}{\left(4z^{4}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}}{4^{-3}\left(z^{4}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}}{4^{-3}z^{-12}}$$

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

$$\frac{\frac{1}{27}}{\frac{1}{64}z^{-12}}$$

Express \frac{\frac{1}{27}}{\frac{1}{64}z^{-12}} as a single fraction.

$$\frac{1}{27\times \frac{1}{64}z^{-12}}$$

Multiply 27 and \frac{1}{64} to get \frac{27}{64}.

$$\frac{1}{\frac{27}{64}z^{-12}}$$