I keep getting different answers, can someone help?

(16^sqrt5)
---------------- * 32^-2sqrt5
(4^sqrt5)

By the way, I got 2^-8sqrt5

You notation is unclear and confusing.

Do you mean 16 to the power of the square root of 5 divided by 4 to the power of the square root of the square root of 5, all multiplied by 32 to the power of -2 times the square root of 5?

If so, I don't know what to do to find a solution. If not, please repost with clearer notation.

I hope this helps. Thanks for asking.

To simplify the expression (16^sqrt5)/(4^sqrt5)*(32^-2sqrt5), we can use the properties of exponents. Let's break it down step by step:

Step 1: Simplify the numerator (16^sqrt5) and the denominator (4^sqrt5) separately.

First, let's work on the numerator (16^sqrt5):
Since 16 can be written as 4^2, we can rewrite the numerator as (4^2)^sqrt5.
Applying the rule of exponents, we multiply the exponents: 2 * sqrt5 = 2sqrt5.
So, the numerator simplifies to 4^2sqrt5.

Now, let's simplify the denominator (4^sqrt5):
We can rewrite the denominator as 2^2sqrt5, as 4 can be written as 2^2.
No further simplification is needed.

Step 2: Combine the simplified numerator and denominator.

When we divide two expressions with the same base, we can subtract the exponents:
(4^2sqrt5) / (2^2sqrt5) = 4^(2sqrt5 - 2sqrt5) = 4^0.
Any non-zero number raised to the power of 0 is equal to 1.

So, the expression simplifies to 1 * (32^-2sqrt5).

Step 3: Simplify the remaining expression.

For simplicity, write 32 as 2^5:
(2^5)^-2sqrt5 = 2^(5 * -2sqrt5) = 2^-10sqrt5.

Therefore, the final simplified expression is 2^-10sqrt5.

In conclusion, you were correct in simplifying the original expression to 2^-10sqrt5.