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

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

Evaluate

$$\frac{1594323}{200}=7971.615$$

Solution Steps

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

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

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

$$\frac{3^{13}}{2^{3}\times 5^{2}}$$

Calculate 3 to the power of 13 and get 1594323.

$$\frac{1594323}{2^{3}\times 5^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{1594323}{8\times 5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{1594323}{8\times 25}$$

Multiply 8 and 25 to get 200.

$$\frac{1594323}{200}$$

Factor

$$\frac{3 ^ {13}}{2 ^ {3} \cdot 5 ^ {2}} = 7971\frac{123}{200} = 7971.615$$