Solve (1/4^222)(2^111)

$$( \frac { 1 } { 4 ^ { 222 } } ) ( 2 ^ { 111 } )$$

Evaluate

$$\frac{1}{17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592}\approx 5.714936956 \cdot 10^{-101}$$

Solution Steps

Calculate 4 to the power of 222 and get 45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416.

$$\frac{1}{45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416}\times 2^{111}$$

Calculate 2 to the power of 111 and get 2596148429267413814265248164610048.

$$\frac{1}{45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416}\times 2596148429267413814265248164610048$$

Multiply \frac{1}{45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416} and 2596148429267413814265248164610048 to get \frac{2596148429267413814265248164610048}{45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416}.

$$\frac{2596148429267413814265248164610048}{45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416}$$

Reduce the fraction \frac{2596148429267413814265248164610048}{45427420268475430659332737993000283397102585042957378767593137448789955507087370207886940669610222847547657600391636120845912601788416} to lowest terms by extracting and canceling out 2596148429267413814265248164610048.

$$\frac{1}{17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592}$$

Factor

$$\frac{1}{2 ^ {333}} = 5.714936956411375 \times 10^{-101}$$