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

1 Answer
Jun 25, 2017

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 :)