Solve (frac{14e^{-2}k^-1}{2e^2k^-1})^-2

$$( \frac { 14 e ^ { - 2 } k ^ { - 1 } } { 2 e ^ { 2 } k ^ { - 1 } } ) ^ { - 2 }$$

Evaluate

$$\frac{e^{8}}{49}\approx 60.835877287$$

Solution Steps

Cancel out 2\times \frac{1}{k} in both numerator and denominator.

$$\left(\frac{7e^{-2}}{e^{2}}\right)^{-2}$$

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

$$\left(\frac{7}{e^{4}}\right)^{-2}$$

To raise \frac{7}{e^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{7^{-2}}{\left(e^{4}\right)^{-2}}$$

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

$$\frac{7^{-2}}{e^{-8}}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{\frac{1}{49}}{e^{-8}}$$

Express \frac{\frac{1}{49}}{e^{-8}} as a single fraction.

$$\frac{1}{49e^{-8}}$$

Expand

$$\frac{e^{8}}{49}$$

Solution Steps

Cancel out 2\times \frac{1}{k} in both numerator and denominator.

$$\left(\frac{7e^{-2}}{e^{2}}\right)^{-2}$$

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

$$\left(\frac{7}{e^{4}}\right)^{-2}$$

To raise \frac{7}{e^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{7^{-2}}{\left(e^{4}\right)^{-2}}$$

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

$$\frac{7^{-2}}{e^{-8}}$$

Calculate 7 to the power of -2 and get \frac{1}{49}.

$$\frac{\frac{1}{49}}{e^{-8}}$$

Express \frac{\frac{1}{49}}{e^{-8}} as a single fraction.

$$\frac{1}{49e^{-8}}$$