Solve 2^-4*5^-5/5^-72*5^-5

$$\frac { 2 ^ { - 4 } \cdot 5 ^ { - 5 } } { 5 ^ { - 72 } \cdot 5 ^ { - 5 } }$$

Evaluate

$$\frac{211758236813575084767080625169910490512847900390625}{16}=1.32348898 \cdot 10^{49}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -72 and -5 to get -77.

$$\frac{2^{-4}\times 5^{-5}}{5^{-77}}$$

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

$$2^{-4}\times 5^{72}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\frac{1}{16}\times 5^{72}$$

Calculate 5 to the power of 72 and get 211758236813575084767080625169910490512847900390625.

$$\frac{1}{16}\times 211758236813575084767080625169910490512847900390625$$

Multiply \frac{1}{16} and 211758236813575084767080625169910490512847900390625 to get \frac{211758236813575084767080625169910490512847900390625}{16}.

$$\frac{211758236813575084767080625169910490512847900390625}{16}$$

Factor

$$\frac{5 ^ {72}}{2 ^ {4}} = 1.3234889800848442 \times 10^{49}$$