Question

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

Answer 1

`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` :)