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

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

Evaluate

$$\frac{1}{4608}\approx 0.000217014$$

Solution Steps

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

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

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

$$\frac{4^{2}}{2^{13}\times 3^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16}{2^{13}\times 3^{2}}$$

Calculate 2 to the power of 13 and get 8192.

$$\frac{16}{8192\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16}{8192\times 9}$$

Multiply 8192 and 9 to get 73728.

$$\frac{16}{73728}$$

Reduce the fraction \frac{16}{73728} to lowest terms by extracting and canceling out 16.

$$\frac{1}{4608}$$

Factor

$$\frac{1}{2 ^ {9} \cdot 3 ^ {2}} = 0.00021701388888888888$$