How do you simplify #(2^-1)(4^3)(8^-1)# with a base of 2?

1 Answer
Jun 25, 2017

Answer:

#2^2#

Explanation:

Rewrite each exponent with a base of 2. To do this, you need to find an equivalent to the current base.

  • #2^-1# already has a base of two, so we can leave that one alone.

  • #4^3# is also equal to #2^(2*3)#, since #4# is equal to #2^2#

  • #8^-1# is also equal to #2^(3*-1)#, since #8# is equal to #2^3#

Our expression is now:

#(2^-1)(2^(2*3))(2^(3*-1))#
= #(2^-1)(2^6)(2^-3)#

When multiplying powers with the same base, add the exponents.

Adding the exponents: #-1 + 6 - 3 = 2#

#= 2^2#
#=4#

If you want your answer as a base of 2, then keep it as #2^2# :)