How do you simplify #5^(2/3) * 5^(4/3)#?

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Answer 1 · 2018-04-05T02:27:11

#5^(2/3) * 5^(4/3)# can be simplified to #25#.

By exponent laws, #x^a*x^b = x^(a+b)#.

#5^(2/3) * 5^(4/3)#
#=5^(2/3+4/3)#
#=5^(6/3)#
#=5^2#
#=25#

Answer 2 · 2018-04-05T02:27:58

#color(green)(=> 5^(2)#

Given #5^(2/3) * 5 ^ (4/3)#

As per the theory of inices,

#x^m * x ^n = x^ (m + n)#

#:. => 5 ^ ((2/3) + (4/3))#

#=> 5 ^ ((2+4)/3), " taking 3 as LCM "#

#=> 5^(6/3) " or " 5^(2)#