Solve frac{2^{5}*3^{3}*5^-3}{3^-6*2^-1*5^2}

$$\frac { 2 ^ { 5 } \times 3 ^ { 3 } \times 5 ^ { - 3 } } { 3 ^ { - 6 } \times 2 ^ { - 1 } \times 5 ^ { 2 } }$$

Evaluate

$$\frac{1259712}{3125}=403.10784$$

Solution Steps

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

$$\frac{2^{6}\times 3^{9}\times 5^{-3}}{5^{2}}$$

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

$$\frac{2^{6}\times 3^{9}}{5^{5}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{64\times 3^{9}}{5^{5}}$$

Calculate 3 to the power of 9 and get 19683.

$$\frac{64\times 19683}{5^{5}}$$

Multiply 64 and 19683 to get 1259712.

$$\frac{1259712}{5^{5}}$$

Calculate 5 to the power of 5 and get 3125.

$$\frac{1259712}{3125}$$

Factor

$$\frac{2 ^ {6} \cdot 3 ^ {9}}{5 ^ {5}} = 403\frac{337}{3125} = 403.10784$$