If #x# and #y# are positive integers and #3^(2x) * 3^(2y) = 81#, what is the value of #x+y#?

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Answer 1 · 2016-02-13T17:52:12

#color(blue)(x+y=2#

#3^(2x) xx 3^(2y) = 81#

#color(blue)(81= 9xx9#

( note: #9 # can be conveniently expressed as a power of #3#)

#3^(2x) xx 3^(2y) = 9 xx 9= 3^2 xx 3^2#

#3^(2x) xx 3^(2y) = 3^2 xx 3^2#

Equating powers:
#2x =2, color(blue)(x=1#
#2y=2, color(blue)(y=1#

#color(blue)(x+y=2#