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#.