How do you solve #6^{- 1} \cdot 6^{- 2}#?

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Answer 1 · 2016-10-06T13:39:09

#color(green)(1/256#

#color(blue)(6^-1*6^-2#

There are two ways to solve it

Recall

#1)# #color(brown)(x^-y=1/x^y#

#2)# #color(brown)(x^y*x^z=x^(y+z)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#:.6^-1*6^-2=1/6^1*1/6^2#

#rarr1/6*1/36#

#rarr(1*1)/(6*36)#

#color(green)(rArr1/216#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#:.6^-1*6^-2=6^(-1+ -2)#

#rarr6^-3#

#rarr1/6^3#

#color(green)(rArr1/216#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So,

#color(green)(6^-1*6^-2=1/256#