Question

Convert Following expression in radical form into an exponential expression in rational form, multiply and simplify then divide you do not need to evaluate just put in simplest form

Answer 1

5 7/5

Explanation:

As you can see there is a divisions sign so you will start there.

The square root of 5^6 will turn into 5 6/2 divided by 5 3/5.

You want to find the LCD for the denominator. That will be 10, 6 divided by 3 equals 2 so you will have 5 7/2 times 5 2/10. You then change the two to a 10 and multiply the 7 and 2 which will become 5 14/10.

Once simplified the answer is 5 7/5.

Hope this helps :)

Answer 2

9.

`\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}`

Using the following properties:

`\begin{gathered} x^a\cdot x^b=x^(a+b) \\ a^(-x)=(1)/(a^x) \\ \sqrt[z]{x^y}=x^{(y)/(z)} \end{gathered}`
`\frac{\sqrt[]{5^7}\cdot\sqrt[]{5^6}}{\sqrt[5]{5^3}}=5^{(7)/(2)}\cdot5^{(6)/(2)}\cdot5^{-(3)/(5)}=5^{(7)/(2)+(6)/(2)-(3)/(5)}=5^{(59)/(10)}`