How do you write a surd as an exponential with a different base? How do you get from √128 to 2^(7/2)?

Question

Hello! 

The question in my textbook asks me to find m when √128 = 2^m

 

I used an app to solve the question and writing “√128 as an exponential with a base of 2“ was one of the steps

Please help me understand how to get to 2^(7/2)! 

 

Thank you in advance!

 

 

Answer 1

√128=√(2*2*2*2*2*2*2)=√(2⁷)

the square root a number is the same as the number raised to the (1/2) power; 2 is understood to be the index of the radical when no index is written, that is, square root

for example, √36=36^(1/2) (which equals 6)

therefore, √(2⁷)=(2⁷)^(1/2)

when you have a power raised to a power you multiply the exponents

therefore, (2⁷)^(1/2)=2^(7/2) because 7*(1/2)=7/2

in 7/2, 2 is the index and 7 is the power of 2