can someone check my answer on this one?
rewrite with rational exponents:
(sqrt5mn)^9
i got: 5^9/2m^9/2n^9/2 is this correct?
It is correct, good work. Ignore the immatures.
Thank you Bob: Did it make any difference that everything inside the radical is in parentheses? Could the answer have been 5mn^9/2. What did the parentheses indicate?
To rewrite (sqrt(5mn))^9 with rational exponents, we can use the property that (a^m)^n = a^(m * n).
First, let's rewrite sqrt(5mn) as (5mn)^(1/2).
Now, applying the property, we have [(5mn)^(1/2)]^9.
To raise a power to another power, multiply the exponents, so we get (5mn)^((1/2) * 9).
Simplifying further, we have (5mn)^(9/2), which can also be written as 5^(9/2) * m^(9/2) * n^(9/2).
Therefore, your answer (5^(9/2) * m^(9/2) * n^(9/2)) is correct!