Question

Write each expression below in radical form and compute the value without using a calculator.

a. 25 5/2
b. 81 7/4

Answer 1

Assuming that an exponentiation sign is missing, all you need to know is that rational exponents work like this:

`a^{(b)/(c)}=\sqrt[c]{a^b}`

So, you have

`25^{(5)/(2)}=√(25^5)=√((5^2)^5)=5^5`

And similarly,

`81^{(7)/(4)}=\sqrt[4]{25^7}=\sqrt[4]{(3^4)^7}=3^7`