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

2 Answers
Sep 23, 2017

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

Sep 23, 2017

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.