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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 2: Passport to advanced mathematics- Solving quadratic equations — Basic example
- Solving quadratic equations — Harder example
- Interpreting nonlinear expressions — Basic example
- Interpreting nonlinear expressions — Harder example
- Quadratic and exponential word problems — Basic example
- Quadratic and exponential word problems — Harder example
- Manipulating quadratic and exponential expressions — Basic example
- Manipulating quadratic and exponential expressions — Harder example
- Radicals and rational exponents — Basic example
- Radicals and rational exponents — Harder example
- Radical and rational equations — Basic example
- Radical and rational equations — Harder example
- Operations with rational expressions — Basic example
- Operations with rational expressions — Harder example
- Operations with polynomials — Basic example
- Operations with polynomials — Harder example
- Polynomial factors and graphs — Basic example
- Polynomial factors and graphs — Harder example
- Nonlinear equation graphs — Basic example
- Nonlinear equation graphs — Harder example
- Linear and quadratic systems — Basic example
- Linear and quadratic systems — Harder example
- Structure in expressions — Basic example
- Structure in expressions — Harder example
- Isolating quantities — Basic example
- Isolating quantities — Harder example
- Function notation — Basic example
- Function notation — Harder example

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# Radicals and rational exponents — Basic example

Watch Sal work through a basic Radicals and rational exponents problem.

## Want to join the conversation?

- Why did Sal stop saying “good luck test takers”

It was really a big time motivation(19 votes) - Exam in 1 day and I dont know anything. sigh(13 votes)
- how did it go for you?(2 votes)

- Good luck to everyone on their SAT!(12 votes)
- Is there any way to practice this on here because that is what I really need to do.(7 votes)
- For the SAT test? If so, you can start here: https://www.khanacademy.org/mission/sat/practice(4 votes)

- If you multiply the same square root with itself does it always just give you the number? For eg. (sqroot 2) * (sqroot 2) = 2.(3 votes)
- Yes. When you take the square root of something, you ask "What number multiplied by itself gives me my input?". When you take this number and multiply it by itself, like in the equation you so kindly provided, by definition you should get the input.(4 votes)

- if sqroot times sqroot is a whole number then how come when he multiplied the decimals in the sqroots it didn't come out as 0.5 but as a root 0.5(3 votes)
- You don't quite have it down.

Like Sal shows sqrt(a) * sqrt(b) = sqrt(a * b).

If both radicals are the same (a = b), then your case will be true. e.g.:`sqrt(4) * sqrt(4) = sqrt(4 * 4) = 4`

I believe you were thinking of*perfect squares*, such as the example I just gave.

Hope this helps!

- Convenient Colleague(4 votes)

- why didn't we multiply 3 and 1/3 to get 1 what...(4 votes)
- That's because we multiply bases only when their exponents are the same and in general we multiply their coefficients.(2 votes)

- Why does the (1/3) become 3^-1?(2 votes)
- Using x, we know that 1/x is the same as x^-1. This is because the two of them represent an inverse of x. Reciprocal numbers/functions and negative indices work the same way.(2 votes)

- Does the SAT consider plus or minus of an answer for a square root of a number or is it always positive? Ex: (square root of 4) = -2, so +/-2=-2, or does the SAT accept the answer +2 does not equal to -2.(2 votes)

## Video transcript

- [Instructor] Which
of the following values is equal to the value above? And we've got this expression here with a bunch of negative
fractional exponents. And at first, you might say okay, how do I deal with this? I don't know that the
fifth root of three is, much less the negative fifth root, and this one third to
the negative two fifths. How do I simplify this? And the key realization here, is that one third is the same thing as three to the negative one power. One third is the same thing as three to the negative one power. And if we do that, I suspect that we're gonna be able to get similar bases here. Let me rewrite the whole thing. So, it's gonna be three
to the negative one fifth times, instead of writing one third, I can write three to
the negative one power, to the negative two fifths power. And now we can just use up
our straight exponent rules to simplify things a little bit. So this business right over here, that I'm squaring in this orange color, if I raise something to an exponent, and then raise it again
to another exponent, that's going to be the
same thing as taking our original raise and
raising it to the negative one times the negative one times
negative two fifths power. So if I raise it to the negative one, and then the negative two fifths, that's the same thing as raising three to the negative one times
negative two fifths power. And so this over here is sill going to be three to the negative one fifth. And so this is going to be equal to three to the negative one fifth times, now negative one times
negative two fifths, that's going to be positive two fifths. So we times three to the two fifths. And now we have a situation where we have the same base. We have the product of three
to the negative one fifth times three to the positive two fifths. This is going to be equal to, we can take our base three, is gonna be three to
the negative one fifth plus two fifths power,
plus two fifths power. If you have the same base, the product of that base
raised to one exponent and that same base raised
to another exponent, that's the same thing as
that base raised to the sum of those exponents, a
classic exponent property. I encourage you to go on Khan Academy if this is looking foreign
or if you need some review. But now this is pretty straightforward. This is going to be equal to, this is is going to be equal
to three to the negative one fifth plus two
fifths is just one fifth. And there you have it: three to the one fifth power.