Solve 2^31(1+16)/2^-6(frac{1{16}+1)}

$$\frac { 2 ^ { 31 } ( 1 + 16 ) } { 2 ^ { - 6 } ( \frac { 1 } { 16 } + 1 ) }$$

Evaluate

$$2199023255552$$

Solution Steps

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

$$\frac{2^{37}\left(1+16\right)}{\frac{1}{16}+1}$$

Calculate 2 to the power of 37 and get 137438953472.

$$\frac{137438953472\left(1+16\right)}{\frac{1}{16}+1}$$

Add 1 and 16 to get 17.

$$\frac{137438953472\times 17}{\frac{1}{16}+1}$$

Multiply 137438953472 and 17 to get 2336462209024.

$$\frac{2336462209024}{\frac{1}{16}+1}$$

Add \frac{1}{16} and 1 to get \frac{17}{16}.

$$\frac{2336462209024}{\frac{17}{16}}$$

Divide 2336462209024 by \frac{17}{16} by multiplying 2336462209024 by the reciprocal of \frac{17}{16}.

$$2336462209024\times \frac{16}{17}$$

Multiply 2336462209024 and \frac{16}{17} to get 2199023255552.

$$2199023255552$$

Factor

$$2^{41}$$