Solve 2^3*8^-100*4^200*2^-101

$$2 ^ { 3 } \times 8 ^ { - 100 } \times 4 ^ { 200 } \times 2 ^ { - 101 }$$

Evaluate

$$4$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -101 to get -98.

$$2^{-98}\times 8^{-100}\times 4^{200}$$

Calculate 2 to the power of -98 and get \frac{1}{316912650057057350374175801344}.

$$\frac{1}{316912650057057350374175801344}\times 8^{-100}\times 4^{200}$$

Calculate 8 to the power of -100 and get \frac{1}{2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376}.

$$\frac{1}{316912650057057350374175801344}\times \frac{1}{2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376}\times 4^{200}$$

Multiply \frac{1}{316912650057057350374175801344} and \frac{1}{2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376} to get \frac{1}{645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344}.

$$\frac{1}{645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344}\times 4^{200}$$

Calculate 4 to the power of 200 and get 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376.

$$\frac{1}{645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344}\times 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376$$

Multiply \frac{1}{645562469521727147413979793000752968582426448207305878207664839135161905504210298657411338320034457858975792993186873344} and 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376 to get 4.

$$4$$

Factor

$$2^{2}$$