(9n^4)^(1/2)= 3n??
3 n^2 = 3 n
n^2 - n = 0
n(n-1) = 0
n = 0 or n = 1
Not quite
9^(1/2) = 3
but
(n^4)^(1/2) = n^2
so the answer is 3n^2
Is that 3 n not on the right or is that the student's attempt at an answer?
Only the student can tell what was intended. We've provided two solutions, so our work is done here.
The math is much easier than the mind reading.
To simplify the expression (9n^4)^(1/2), we can use the property of exponents which states that raising a number to the power of 1/2 is equivalent to taking its square root.
Let's break down the expression step by step:
1. Start with (9n^4)^(1/2).
2. Apply the property of exponents: (a^m)^n = a^(m*n) to get 9^(1/2) * (n^4)^(1/2).
3. Simplify 9^(1/2) to its square root, which is 3.
4. Simplify (n^4)^(1/2) to the square root of n^4, which is n^2.
- This is because when we raise n^4 to the power of 1/2, we are essentially taking the square root of n^4. Since n^4 is already a perfect square, the result is n^2.
Putting it all together, we have 3 * n^2, which is equal to 3n^2. Therefore, the simplification of (9n^4)^(1/2) is 3n^2, not 3n.