Given #p=2^x# and #q = 2^y#, how do you express #8^(x+y)/4^x# in terms of #p and q#?

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Answer 1 · 2017-08-15T13:23:40

#p q^(3)#

We have: #frac(8^(x + y))(4^(x))#

Let's express the numerator and denominator in terms of #2#:

#= frac((2^(3))^(x + y))((2^(2))^(x))#

Using the laws of exponents:

#= frac((2^(x + y))^(3))((2^(x))^(2))#

#= frac((2^(x) cdot 2^(y))^(3))((2^(x))^(2))#

Then, let's replace #2^(x)# and #2^(y)# with #p# and #q#, respectively:

#= frac((p cdot q)^(3))(p^(2))#

#= frac(p^(3) cdot q^(3))(p^(2))#

#= p^(3 - 2) cdot q^(3)#

#= p^(1) cdot q^(3)#

#= p q^(3)#