Question

Simplify `9^(5/2)+4/5`?

Answer 1

`root(10)(9^33)`

Explanation:

I'm going to assume you meant `9^(5/2+4/5)`

I'm also going to assume you wanted to get rid of the fractional exponent.

Let's do this!

First, simplify the sum by finding the Lowest Common Denominator (LCD) of the two fractions.

Since one is `5/color(red)(2)` and the other is `4/color(red)(5)`,
`color(red)(10)` is the lowest number that both `2` and `5` goes in.

So let's rewrite that.

`25/10` for the first term because to get to 10 from 2, you have to multiply by 5. So you multiply the numerator (5) by `5` as well.

`8/10` for the first term because to get to 10 from 5, you have to multiply by 2. So you multiply the numerator (4) by `2` as well.

We get:
`25/10+8/10`

`=(25+8)/10`

`=33/10`

So our original expression becomes `9^(33/10)`

To get rid of the fractional exponent, there is this handy rule:

So we can rewrite our expression as:

`root(10)(9^33)`

Answer 2

`9^(5/2)+4/5=244.25`

Explanation:

`9^(5/2)+4/5`

= `(3^2)^(5/2)+4/5`

= `3^(2*5/2)+5/4`

= `3^5+1.25`

= `243+1.25`

= `244.25`