Solve frac{2^{-8}*3^{5}*5^-6}{2^-7*3^6*5^-5}

$$\frac { 2 ^ { - 8 } \cdot 3 ^ { 5 } \cdot 5 ^ { - 6 } } { 2 ^ { - 7 } \cdot 3 ^ { 6 } \cdot 5 ^ { - 5 } }$$

Evaluate

$$\frac{1}{30}\approx 0.033333333$$

Solution Steps

Cancel out 3^{5} in both numerator and denominator.

$$\frac{2^{-8}\times 5^{-6}}{3\times 2^{-7}\times 5^{-5}}$$

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

$$\frac{1}{3\times 2^{1}\times 5^{1}}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{1}{3\times 2\times 5^{1}}$$

Multiply 3 and 2 to get 6.

$$\frac{1}{6\times 5^{1}}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{1}{6\times 5}$$

Multiply 6 and 5 to get 30.

$$\frac{1}{30}$$

Factor

$$\frac{1}{2 \cdot 3 \cdot 5} = 0.03333333333333333$$