Solve (frac{k^{3}l^{-5}m}{k^4l^-7m^-3})^-2

$$( \frac { k ^ { 3 } l ^ { - 5 } m } { k ^ { 4 } l ^ { - 7 } m ^ { - 3 } } ) ^ { - 2 }$$

Evaluate

$$\frac{k^{2}}{l^{4}m^{8}}$$

Solution Steps

Cancel out k^{3} in both numerator and denominator.

$$\left(\frac{l^{-5}m}{l^{-7}m^{-3}k}\right)^{-2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{l^{2}m^{4}}{k}\right)^{-2}$$

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

$$\frac{\left(l^{2}m^{4}\right)^{-2}}{k^{-2}}$$

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

$$\frac{\left(l^{2}\right)^{-2}\left(m^{4}\right)^{-2}}{k^{-2}}$$

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

$$\frac{l^{-4}\left(m^{4}\right)^{-2}}{k^{-2}}$$

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

$$\frac{l^{-4}m^{-8}}{k^{-2}}$$

Expand

$$\frac{k^{2}}{l^{4}m^{8}}$$

Solution Steps

Cancel out k^{3} in both numerator and denominator.

$$\left(\frac{l^{-5}m}{l^{-7}m^{-3}k}\right)^{-2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{l^{2}m^{4}}{k}\right)^{-2}$$

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

$$\frac{\left(l^{2}m^{4}\right)^{-2}}{k^{-2}}$$

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

$$\frac{\left(l^{2}\right)^{-2}\left(m^{4}\right)^{-2}}{k^{-2}}$$

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

$$\frac{l^{-4}\left(m^{4}\right)^{-2}}{k^{-2}}$$

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

$$\frac{l^{-4}m^{-8}}{k^{-2}}$$