86,760 views
33 votes
33 votes
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

Convert Following expression in radical form into an exponential expression in rational-example-1
User Olatunde Garuba
by
2.6k points

2 Answers

10 votes
10 votes

Answer:

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 :)

User Pablo Guerrero
by
2.9k points
23 votes
23 votes

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)}

User Kay Zed
by
2.5k points