Solve (4k^2/n^2)^-3=

$$( \frac { 4 k ^ { 2 } } { n ^ { 2 } } ) ^ { - 3 } =$$

Evaluate

$$\frac{\left(\frac{n}{k}\right)^{6}}{64}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{\left(4k^{2}\right)^{-3}}{n^{-6}}$$

Expand \left(4k^{2}\right)^{-3}.

$$\frac{4^{-3}\left(k^{2}\right)^{-3}}{n^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{4^{-3}k^{-6}}{n^{-6}}$$

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

$$\frac{\frac{1}{64}k^{-6}}{n^{-6}}$$

Expand

$$\frac{\left(\frac{n}{k}\right)^{6}}{64}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{\left(4k^{2}\right)^{-3}}{n^{-6}}$$

Expand \left(4k^{2}\right)^{-3}.

$$\frac{4^{-3}\left(k^{2}\right)^{-3}}{n^{-6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{4^{-3}k^{-6}}{n^{-6}}$$

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

$$\frac{\frac{1}{64}k^{-6}}{n^{-6}}$$