Solve frac{5^{-4}*2^-2}{2^-3*5^-5*2^5}

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

Evaluate

$$\frac{5}{16}=0.3125$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and 5 to get 2.

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

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

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

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

$$\frac{5^{1}}{2^{4}}$$

Calculate 5 to the power of 1 and get 5.

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

Calculate 2 to the power of 4 and get 16.

$$\frac{5}{16}$$

Factor

$$\frac{5}{2 ^ {4}} = 0.3125$$