Solve 4^{-4}*49^{2}*5^-3+(-3^-1+2^-2)^-1

$$4 ^ { - 4 } \cdot 49 ^ { 2 } \cdot 5 ^ { - 3 } + ( - 3 ^ { - 1 } + 2 ^ { - 2 } ) ^ { - 1 }$$

Evaluate

$$-\frac{381599}{32000}=-11.92496875$$

Solution Steps

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{1}{256}\times 49^{2}\times 5^{-3}+\left(-3^{-1}+2^{-2}\right)^{-1}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{1}{256}\times 2401\times 5^{-3}+\left(-3^{-1}+2^{-2}\right)^{-1}$$

Multiply \frac{1}{256} and 2401 to get \frac{2401}{256}.

$$\frac{2401}{256}\times 5^{-3}+\left(-3^{-1}+2^{-2}\right)^{-1}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{2401}{256}\times \frac{1}{125}+\left(-3^{-1}+2^{-2}\right)^{-1}$$

Multiply \frac{2401}{256} and \frac{1}{125} to get \frac{2401}{32000}.

$$\frac{2401}{32000}+\left(-3^{-1}+2^{-2}\right)^{-1}$$

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

$$\frac{2401}{32000}+\left(-\frac{1}{3}+2^{-2}\right)^{-1}$$

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

$$\frac{2401}{32000}+\left(-\frac{1}{3}+\frac{1}{4}\right)^{-1}$$

Add -\frac{1}{3} and \frac{1}{4} to get -\frac{1}{12}.

$$\frac{2401}{32000}+\left(-\frac{1}{12}\right)^{-1}$$

Calculate -\frac{1}{12} to the power of -1 and get -12.

$$\frac{2401}{32000}-12$$

Subtract 12 from \frac{2401}{32000} to get -\frac{381599}{32000}.

$$-\frac{381599}{32000}$$

Factor

$$-\frac{381599}{32000} = -11\frac{29599}{32000} = -11.92496875$$