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Mathematics
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Problem 1. Do you know the definition of a rational (fraction) exponent?
@mathstudent55 im afraid i don't

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\(\Huge a^{\frac{m}{n}} = \sqrt[n] {a^m} = (\sqrt[n]a)^m\)
To find a rational power of a number, raise the number to the numerator of the exponent and take the root of the number the denominator tells you.
Keep in mind: numerator -------> exponent denominator -----> root
Examples: |dw:1438493658565:dw|
|dw:1438493695962:dw|
|dw:1438493741614:dw|
Do you understand the examples?
All the examples show you the same idea. The denominator of the exponent tells you which root to take. When the denominator is 2, you take the square root. When the denominator is 3 you take the cubic root, etc.
The numerator tells you what power to raise the number to before or after you take the root.
yes. i do. what i don't get is that when you get the result you get a single number, but my answer choices have the square root symbol would what you showed me still apply?
Let's look at problem 1 now together.
|dw:1438494095419:dw|
What does the 2 in the denominator mean?
numerator?
From above: "The denominator of the exponent tells you which root to take."
"When the denominator is 2, you take the square root. "
A denominator of 2 means take the square root. |dw:1438494212377:dw|
The numerator of 3 means raise the number to the 3rd power.
What is \(2^3\) equal to?
8. but what do you do with the denominator in the fraction?
|dw:1438494329059:dw|
The denominator of the exponent changed the problem from an exponent problem to a root problem.
|dw:1438494376526:dw|
OOHHHHHHHHHH OMG IM SO STUPIDDDD LOL
No, you're not stupid. You're learning. I went through the same process you are going through now.
Are you ready for problem 2?
yup
Here you will need a property of exponents. Here it is: \(\Huge \dfrac{a^m}{a^n} = a^{m - n} \) When you divide powers with the same base, write the same base and subtract the exponents.
Here is an example of this rule: |dw:1438494620860:dw| Do you underrstand the example?
yes
OK. Now lets do problem 2.
The first step is to use the rational exponents in reverse. Earlier, I explained how to handle a fraction as an exponent. In this problem, you are given a root in the numerator and a root in the denominator. We need to use the rule of rational exponents in reverse, and write the numerator and denominator of this fraction with fractions for the exponents.
Let's just look at the numerator of our problem.
|dw:1438494930324:dw|
|dw:1438495081620:dw| We need to replace the box with an exponent. You need to work backwards, and figure out what fraction you need to raise 7 to to get the cubic root of 7. Remember above we saw that the denominator of an exponent tells you which root to take. Here we see we are taking the 3rd root (called the cubic root) of 7. If we take the cubic root of 7, what do we need in the denominator of the exponent?
3?
|dw:1438495150225:dw|
Exaclty. Also, since we have just 7, not 7 raised to some power, that means the numerator is 1.
|dw:1438495224736:dw|
|dw:1438495237856:dw| Ok?
alright
Now let's look at the denominator. The denominator is similar to the numerator except instead of the cubic root, it's the fifth root.
|dw:1438495324943:dw| What fraction is the exponent of 7?
|dw:1438495375343:dw|
|dw:1438495456106:dw| would this be it?
Correct. Now let's put it together the way the problem is given. |dw:1438495483142:dw|
Now you need the rule I gave you above. What do you do when you dived powers with the same base? You subtract the exponents. |dw:1438495589942:dw| What goes in the box?
2/15 ?
|dw:1438495725285:dw|
Correct.
thank you! can you help me with 1 last question?
You're welcome. Sure, one more.
Have you learned how to solve systems of equations by the addition method?
im afraid not
wouldn't the value of y be 8?
We need to solve the system.
wait i got this question. i sent the wrong picture wow
Have you learned how to solve a system of equations by the substitution method?
this was the one
@mathstudent55 well turns out i did because in the snapshot there was no answer. but then i check on my page and it had the answer on it, so i probably figured out this morning
Ok. I see.
The graph of \(y = \sqrt x\) looks like this: |dw:1438496300889:dw|
When you replace x by x - k, where k is a number, the graph shifts horizontally (left or right) k units.
|dw:1438496428565:dw|
If you compare \(y = \sqrt x\) with \(y = \sqrt{x + 7} \), you see that x was replaced by x + 7. That means that when you compare x + 7 with x - k, you see that it equals x - (-7). k = -7. Since k is a negative number, it means the graph shifts to the left. The 7 tells you it is a shift of 7 units left.
|dw:1438496631995:dw|
b and d are giving me some strong feelings for some reason. both of them feel right
From the graphs of the choices, you see that: B is shifted 6 units left D is shifted 7 units left.
d?
@arindameducationusc do you know what the answer would be??
For question 1, 3 is for square power and 2 is for square root power... so apply that
@arindameducationusc im afraid i have already answered question 1. I'm sorry for not informing you . i need 2
Just follow mathstudent steps... He is right

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