I am taking my Algebra Semester exam, and I would really like the answers to the test-
There are 50 questions.
The first question is
What is a simpler form of the radical expression?
4 Sqrt 2401x^12y^16
First, recall that √x^2 = x.
Also, recall that √(xy) = √x * √y
So, if you want to factor an x out of an expression, you need to factor x^2 out of a square root. That means you just divide all the powers by 2. If there are odd powers inside the √, then there will be one left over, staying inside the √. That is √x^7 = √(x^6*x) = √x^6 * √x = x^3 √x
We have 4√(2401x^12y^16)
= 4√(49^2 * x^12 * y^16)
= 4(49 x^6 y^8)
= 196 x^6 y^8
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I understand that you may be looking for the answers to your Algebra semester exam, but providing or seeking unauthorized assistance is considered cheating and goes against ethical principles. It is important to approach your exams with honesty and integrity.
Instead, I can help you understand how to simplify the given radical expression: 4√(2401x^12y^16).
To simplify a radical expression, we look for perfect square factors inside the radical.
First, we simplify the √(2401) because it is a perfect square. 2401 is equal to 49 squared (49 * 49). So 4√(2401x^12y^16) becomes 4 * 49 * √(x^12y^16).
Next, we simplify the x^12. Since x^12 = (x^6)^2, we can simplify further. The expression becomes 4 * 49 * √((x^6)^2y^16).
Similarly, we can simplify y^16 as (y^8)^2. Our expression becomes 4 * 49 * √((x^6)^2 * (y^8)^2).
Now, we can take each perfect square out of the radical. The expression becomes 4 * 49 * (x^6) * (y^8).
Simplifying further, we have 196 * (x^6) * (y^8).
So, a simpler form of the given radical expression is 196x^6y^8.
It's important to note that on your exam, you should show your work and steps to demonstrate your understanding of the process involved in simplifying radical expressions.