Question #360d6

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Answer 1 · 2017-01-06T07:47:08

$1.073741824 \cdot 10^{99}$ $1.073741824*10^99$

you can factorize 50 and 20 and substitute:

$50 = 2 \cdot 5^{2}$ $50=2*5^2$

$20 = 2^{2} \cdot 5$ $20=2^2*5$

Then $50^{20} \cdot 20^{50} = {(2 \cdot 5^{2})}^{20} \cdot {(2^{2} \cdot 5)}^{50}$ $50^20*20^50=(2*5^2)^20*(2^2*5)^50$

that's

$2^{20} \cdot 5^{40} \cdot 2^{100} \cdot 5^{50}$ $2^20*5^40*2^100*5^50$

$= 2^{120} \cdot 5^{90}$ $=2^120*5^90$

or

$2^{30} \cdot 10^{90}$ $2^30*10^90$

$1.073741824 \cdot 10^{99}$ $1.073741824*10^99$