How do you simplify (3^9)/(3^5)?

1 Answer

There are different ways to write it but the fraction ends up being equal to 81

Explanation:

First keep in mind that when we have an exponent, it means we are multiplying the base by itself the exponent's number of times. So for the question here, 3 is being multiplied by itself 9 times in the numerator and 5 times in the denominator. So I can write it like this:

(3xx3xx3xx3xx3xx3xx3xx3xx3)/(3xx3xx3xx3xx3)

and then we can cancel out some 3s and up seeing that there are four 3s left in the numerator:

(cancel(3xx3xx3xx3xx3)(3xx3xx3xx3))/cancel(3xx3xx3xx3xx3)=3xx3xx3xx3=81

Now we need not have done all this expansion - we can rewrite all this in a different way:

3^9/3^5=(3^5xx3^4)/3^5=(cancel(3^5)xx3^4)/cancel(3^5)=3^4=81

or this way:

3^9/3^5=3^9xx3^-5=3^(9-5)=3^4=81