1) If a^b =x and x^b=y then

A)a^2b =y
B)a^b^2 =y
C)b^a=y
D)(ax)^b=y
E)(ax)^b=x

I got B?

2) If a and b are the coordinates of two points on the number line, then which of the following is equivalent to the statement that the absolute value of the distance from a to b is greater than the absolute value distance from -2 to 6.

A) lal > -2. l b l > 6
B) l a-b l > -8
C) la+2l > lb-6l
D)la-bl >8

I got D?

3) Everyone in Niko’s class has a different birth date. If Niko is the 8th oldest person and the 12th youngest person in his class, how many students were in his class?

I got 21 students

For #1 B is the correct answer :)

For #3 if you just count them...

1st oldest
2nd oldest
3
4
5
6
7
Niko (8th oldest, and 12th youngest)
11th youngest
10th
9th
8th
7th
6th
5th
4th
3rd
2nd
first youngest...
And count those lines you will see the number of students is not 21

1) Let's analyze the given expressions and options step by step to find the correct answer.

Given:
a^b = x ----(1)
x^b = y ----(2)

We need to find an option that gives us the value of 'y' in terms of 'a' and 'b'.

Option A: a^2b = y
This option does not involve the variable 'x', so it is unlikely to be the correct answer.

Option B: a^b^2 = y
This option involves 'b' raised to the power of 2, but does not involve the variable 'x'.

Option C: b^a = y
This option does not involve the variable 'x', so it is unlikely to be the correct answer.

Option D: (ax)^b = y
This option involves both 'a' and 'x'. Notice that we can substitute the value of 'x' from equation (1) into this option to get (a^b)^b = y. This simplifies to a^2b = y, which matches with option A.

Option E: (ax)^b = x
This option involves both 'a' and 'x'. However, when we substitute the value of 'x' from equation (1), we get (a^b)^b = x. This does not match with the given equation (2).

Therefore, the correct answer is option A: a^2b = y.

2) Let's analyze the statement and the options provided to determine the equivalent statement.

Statement: The absolute value of the distance from 'a' to 'b' is greater than the absolute value of the distance from -2 to 6.

In other words, |a - b| > |-2 - 6|.

Let's compare this inequality with the options given:

Option A: |a| > -2, |b| > 6
This option does not involve the variables 'a' and 'b' together, so it does not correctly represent the given statement.

Option B: |a - b| > -8
This option directly represents the given statement, as it compares the absolute value of the difference between 'a' and 'b' with -8. Therefore, the correct answer is option B: |a - b| > -8.

Option C: |a + 2| > |b - 6|
This option does not correctly represent the given statement, as it compares the absolute value of the sum of 'a' and 2 with the absolute value of the difference between 'b' and 6.

Option D: |a - b| > 8
This option does not correctly represent the given statement, as it compares the absolute value of the difference between 'a' and 'b' with 8.

Therefore, the correct answer is option B: |a - b| > -8.

3) Let's solve the problem step by step to find the correct answer.

According to the given information:
- Niko is the 8th oldest person in his class.
- Niko is the 12th youngest person in his class.

From the given information, we can infer that there are 11 students older than Niko and 7 students younger than Niko.

So, the total number of students in Niko's class = 11 (older students) + 1 (Niko) + 7 (younger students) = 19.

Therefore, the correct answer is that there are 19 students in Niko's class, not 21.