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

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

Evaluate

$$\frac{9}{16z^{4}}$$

Solution Steps

Cancel out z in both numerator and denominator.

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

To raise \frac{4z^{2}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4z^{2}\right)^{-2}.

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

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

$$\frac{4^{-2}z^{-4}}{3^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}z^{-4}}{3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{16}z^{-4}}{\frac{1}{9}}$$

Divide \frac{1}{16}z^{-4} by \frac{1}{9} by multiplying \frac{1}{16}z^{-4} by the reciprocal of \frac{1}{9}.

$$\frac{1}{16}z^{-4}\times 9$$

Multiply \frac{1}{16} and 9 to get \frac{9}{16}.

$$\frac{9}{16}z^{-4}$$

Expand

$$\frac{9}{16z^{4}}$$

Solution Steps

Cancel out z in both numerator and denominator.

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

To raise \frac{4z^{2}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4z^{2}\right)^{-2}.

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

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

$$\frac{4^{-2}z^{-4}}{3^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}z^{-4}}{3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{16}z^{-4}}{\frac{1}{9}}$$

Divide \frac{1}{16}z^{-4} by \frac{1}{9} by multiplying \frac{1}{16}z^{-4} by the reciprocal of \frac{1}{9}.

$$\frac{1}{16}z^{-4}\times 9$$

Multiply \frac{1}{16} and 9 to get \frac{9}{16}.

$$\frac{9}{16}z^{-4}$$