SOLUTION: Write the expression using exponent notation. sq.rt. 5z

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Question 201368: Write the expression using exponent notation. sq.rt. 5z
Found 2 solutions by user_dude2008, jsmallt9:
Answer by user_dude2008(1862) About Me  (Show Source):
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
By definition sqrt%285z%29+%2A+sqrt%285z%29+=+5z


Writing this in exponential form, using "y" for the exponent we will figure out, we get:
%285z%29%5Ey+%2A+%285z%29%5Ey+=+%285z%29%5E1


The rule for exponents, when we multiply, is to add the exponents. So we get:
%285z%29%5E%28y%2By%29+=+%285z%29%5E1
which simplifies to:
%285z%29%5E%282y%29+=+%285z%29%5E1
This means that
2y = 1
Dividing both sides by 2:
y+=+1%2F2


Therefore sqrt%285z%29+=+%285z%29%5E%281%2F2%29

Using similar logic we can show that root%283%2C+x%29+=+x%5E%281%2F3%29
root%284%2C+x%29+=+x%5E%281%2F4%29
root%285%2C+x%29+=+x%5E%281%2F5%29
etc.