Solve 2^-45^-5/5^-125^5

$$\frac{ { 2 }^{ -4 } { 5 }^{ -5 } }{ { 5 }^{ -12 } { 5 }^{ 5 } }$$

Evaluate

$$\frac{25}{16}=1.5625$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -12 and 5 to get -7.

$$\frac{2^{-4}\times 5^{-5}}{5^{-7}}$$

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

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

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

$$\frac{1}{16}\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{1}{16}\times 25$$

Multiply \frac{1}{16} and 25 to get \frac{25}{16}.

$$\frac{25}{16}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {4}} = 1\frac{9}{16} = 1.5625$$