Solve frac{5^{-3}4^-3}{3^-26^22^-2}

$$\frac { 5 ^ { - 3 } 4 ^ { - 3 } } { 3 ^ { - 2 } 6 ^ { 2 } 2 ^ { - 2 } }$$

Evaluate

$$\frac{1}{8000}=0.000125$$

Solution Steps

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

$$\frac{\frac{1}{125}\times 4^{-3}}{3^{-2}\times 6^{2}\times 2^{-2}}$$

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

$$\frac{\frac{1}{125}\times \frac{1}{64}}{3^{-2}\times 6^{2}\times 2^{-2}}$$

Multiply \frac{1}{125} and \frac{1}{64} to get \frac{1}{8000}.

$$\frac{\frac{1}{8000}}{3^{-2}\times 6^{2}\times 2^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{8000}}{\frac{1}{9}\times 6^{2}\times 2^{-2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{\frac{1}{8000}}{\frac{1}{9}\times 36\times 2^{-2}}$$

Multiply \frac{1}{9} and 36 to get 4.

$$\frac{\frac{1}{8000}}{4\times 2^{-2}}$$

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

$$\frac{\frac{1}{8000}}{4\times \frac{1}{4}}$$

Multiply 4 and \frac{1}{4} to get 1.

$$\frac{\frac{1}{8000}}{1}$$

Anything divided by one gives itself.

$$\frac{1}{8000}$$

Factor

$$\frac{1}{2 ^ {6} \cdot 5 ^ {3}} = 0.000125$$