Question

How do you simplify `\frac { 2^ { 2} } { 2^ { - 8} }`?

Answer 1

1024

Explanation:

Let's rewrite this equation so that it makes more sense

`2^2/2^-8 = 2^2 -: 2^-8`

Now the let's solve this

The third law of indices tells us that `a^n -: a^m = a^(n-m)` with a being the same bases (not different numbers) and `m and n` are the bases.

`2^color(red)(2- (-8))` which gives us `2^color(green)(10)`

`2^10 = 1024`

Answer 2

Simplify the fraction by turning it into a multiplication expression.

Explanation:

In algebra, if a number or variable has a negative exponent, then it is the same as 1 divided by that number or variable with a positive "version" of the exponent. However, if the denominator of a fraction has a negative exponent, then the denominator is the same as a number with a positive exponent.

In other words, you may know that `2^-x=1/2^x`. The same goes for its inverse; `1/2^-x=2^x`

We have our fraction, `2^2/2^-8`. Since we know that `1/2^-8` would equal `2^8`, let's make a multiplication expression:

`2^2/2^-8=2^2*2^8`

All we have to do from here is add the exponents together, Remember that if two exponents have the same base, they can be added.

`2^2*2^8=2^10`

We now have our answer, `2^10`.