Can you give me the steps for this question

Question

write in the form 5^r, where r is a rational number. 1.)1 2.)1/5 3)(square root 5)^7 4.)3 suare root 255.)square root 1256.)1/ square roor 5

 

 

Can i have the steps and what exactly they are asking by this to write in the form 5^r

Answer 1

1. r = 0 (anything to the 0th power is 1)

2. y = 5^x

   1/5 = 5^x

   x = -1

3. sqrt(5)^7 = 5^x

   x = 7/2

4. cube root (25) = 5^x   --->

25 ^1/3 = 5^x

25= 5^2

x = 2/3

5. sqrt(125) = 5^x

125 = 5^3

125^1/2 = 5^x

5^3/2 = 5^x

x = 3/2

 

6. 1/sqrt(5) = 5^x

5^-1/2 = 5^x

x = -1/2