Solve frac{3^{6}*2^{7}*5^2}{2^10*5^4*3^-8}

$$\frac { 3 ^ { 6 } \times 2 ^ { 7 } \times 5 ^ { 2 } } { 2 ^ { 10 } \times 5 ^ { 4 } \times 3 ^ { - 8 } }$$

Evaluate

$$\frac{4782969}{200}=23914.845$$

Solution Steps

Cancel out 2^{7}\times 5^{2} in both numerator and denominator.

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

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

$$\frac{3^{14}}{2^{3}\times 5^{2}}$$

Calculate 3 to the power of 14 and get 4782969.

$$\frac{4782969}{2^{3}\times 5^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{4782969}{8\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{4782969}{8\times 25}$$

Multiply 8 and 25 to get 200.

$$\frac{4782969}{200}$$

Factor

$$\frac{3 ^ {14}}{2 ^ {3} \cdot 5 ^ {2}} = 23914\frac{169}{200} = 23914.845$$