Solve 25*5^-4/5^-3*40*5^-8

$$\frac { 25 \times 5 ^ { - 4 } } { 5 ^ { - 3 } \times 40 \times 5 ^ { - 8 } }$$

Evaluate

$$\frac{390625}{8}=48828.125$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -8 to get -11.

$$\frac{25\times 5^{-4}}{5^{-11}\times 40}$$

Cancel out 5 in both numerator and denominator.

$$\frac{5\times 5^{-4}}{8\times 5^{-11}}$$

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

$$\frac{5^{-4}\times 5^{12}}{8}$$

To multiply powers of the same base, add their exponents. Add -4 and 12 to get 8.

$$\frac{5^{8}}{8}$$

Calculate 5 to the power of 8 and get 390625.

$$\frac{390625}{8}$$

Factor

$$\frac{5 ^ {8}}{2 ^ {3}} = 48828\frac{1}{8} = 48828.125$$