The product of #(root5 8)##(root3 16)# can be expressed as #2^n#. What is the value of #n#?

1 Answer
sente
Dec 6, 2015

#n = 29/15#

Explanation:

We will use the following properties:

  • #(a^b)^c = a^(bc)#

  • #a^ba^c = a^(b+c)#

#root(5)(8)root(3)(16) = 8^(1/5 )16^(1/3)#

#= (2^3)^(1/5)(2^4)^(1/3)#

#=2^(3/5)2^(4/3)#

#= 2^(3/5 + 4/3)#

#=2^(29/15)#

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