Solve frac{(3e^{-3}f^{-2})^2}{(4e^-1f^-2)^2}

$$\frac { ( 3 e ^ { - 3 } f ^ { - 2 } ) ^ { 2 } } { ( 4 e ^ { - 1 } f ^ { - 2 } ) ^ { 2 } }$$

Evaluate

$$\frac{9}{16e^{4}}\approx 0.010302547$$

Solution Steps

Expand \left(3e^{-3}f^{-2}\right)^{2}.

$$\frac{3^{2}\left(e^{-3}\right)^{2}\left(f^{-2}\right)^{2}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

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

$$\frac{3^{2}e^{-6}\left(f^{-2}\right)^{2}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

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

$$\frac{3^{2}e^{-6}f^{-4}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9e^{-6}f^{-4}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

Expand \left(4e^{-1}f^{-2}\right)^{2}.

$$\frac{9e^{-6}f^{-4}}{4^{2}\left(e^{-1}\right)^{2}\left(f^{-2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{9e^{-6}f^{-4}}{4^{2}e^{-2}\left(f^{-2}\right)^{2}}$$

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

$$\frac{9e^{-6}f^{-4}}{4^{2}e^{-2}f^{-4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9e^{-6}f^{-4}}{16e^{-2}f^{-4}}$$

Cancel out f^{-4} in both numerator and denominator.

$$\frac{9e^{-6}}{16e^{-2}}$$

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

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

Expand

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

Solution Steps

Expand \left(3e^{-3}f^{-2}\right)^{2}.

$$\frac{3^{2}\left(e^{-3}\right)^{2}\left(f^{-2}\right)^{2}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

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

$$\frac{3^{2}e^{-6}\left(f^{-2}\right)^{2}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

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

$$\frac{3^{2}e^{-6}f^{-4}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9e^{-6}f^{-4}}{\left(4e^{-1}f^{-2}\right)^{2}}$$

Expand \left(4e^{-1}f^{-2}\right)^{2}.

$$\frac{9e^{-6}f^{-4}}{4^{2}\left(e^{-1}\right)^{2}\left(f^{-2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{9e^{-6}f^{-4}}{4^{2}e^{-2}\left(f^{-2}\right)^{2}}$$

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

$$\frac{9e^{-6}f^{-4}}{4^{2}e^{-2}f^{-4}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{9e^{-6}f^{-4}}{16e^{-2}f^{-4}}$$

Cancel out f^{-4} in both numerator and denominator.

$$\frac{9e^{-6}}{16e^{-2}}$$

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

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