Question

It turns out that (0.125)^3 can be written as 2^a for some integer a. Find a.

Answer 1

Answer:

$a=-9$

Step-by-step explanation:

We begin with $(0.125)^3$

First, we can convert this decimal into a fraction

$(\frac{1}{8} )^3$

Now, we can simplify the denominator of the fraction

$(\frac{1}{2^{3} } )^3$

Next, we can remove the fraction by rewriting the fraction with a negative power.

$(2^{-3} )^3$

Lastly, we can remove the parenthesis by multiplying the powers together.

$2^{-9}$

This means that $a=-9$