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

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 ${2}^{2 \cdot 3}$, since $4$ is equal to ${2}^{2}$

• ${8}^{-} 1$ is also equal to ${2}^{3 \cdot - 1}$, since $8$ is equal to ${2}^{3}$

Our expression is now:

$\left({2}^{-} 1\right) \left({2}^{2 \cdot 3}\right) \left({2}^{3 \cdot - 1}\right)$
= $\left({2}^{-} 1\right) \left({2}^{6}\right) \left({2}^{-} 3\right)$

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 ${2}^{2}$ :)