Question

Check my answers? I'm taking a little practice quiz and I want to be sure I've got my stuff down pat before moving on to the real thing.

Answer 1

\[\frac{ z ^{3} y ^{4} }{ z ^{5}y }\]

Answer 2

and my answer is z^2 y^3

Answer 3

The y^3 is correct, but not the z part.

Answer 4

is the z part supposed to be negative then?

Answer 5

depends on the instructions

Answer 6

if negative expos are fine, then sure; otherwise we need to place it properly above/below the fraction bar

Answer 7

If you can leave it as a fraction, then both exponents will be positive, but some of it will be in the denominator.

Answer 8

It just says simplify so I suppose I should simplify the negative exponent

Answer 9

I'd leave it as a fraction with positive exponents.

Answer 10

so then 1/z^2 y^3

Answer 11

You know the rule:

\(\large \dfrac{a^m}{a^n} = a ^{m - n} \) ?

Apply it to the z's and to the y's. Then change the one with a negative exponent into a fraction.

Answer 12

Yes.

Answer 13

can you check my next one?

Answer 14

\(\large \dfrac{ z ^{3} y ^{4} }{ z ^{5}y } = z^{-2}y^3 = \dfrac{1}{z^2} \times y^3 = \dfrac{y^3}{z^2} \)

Answer 15

Sure.

Answer 16

oh wait so it's not 1/z^2 y^3 it's y^3/z^2?

Answer 17

They both mean the same, but \(\dfrac{y^3}{z^2}\) is simpler.

Answer 18

so this one is write (3a)^2 without exponents...and ummm the only thing I can come up with is 9a...I don't remember learning this... and then the second part of that is Fill in the blanks (3a)^2 = blank a ^blank...which I don't think I understand what they are asking me to do

Answer 19

Ok.
I'll explain the rule to you.

Answer 20

Here is the rule as a statement in English:
When you raise a product to a power, raise every factor of the product to the power.

Answer 21

Here is the rule as a mathematical expression:

\(\large (ab)^n = a^nb^n\)

Answer 22

Notice the mathematical expression just above. It is very similar to your problem.
If you raise the product ab to power n, you must raise a to the n power and multiply it by b to the n power.
In your case, the product is 3a, and the power is 2.

Answer 23

ok...so let me figure this out...so I have to raise 3^2 and a^2? which gives me me...9a^4because I add the exponent on the a to the one outside the parentheses? (if I sound stupid forgive me I am just trying to figure this out)

Answer 24

No.
You started out correctly.
\(\large (3a)^2 = 3^2a^2\)
Now you can actually calculate \(3^2\) because that is simply \(3 \times 3\).
That means now you have
\(9a^2\)

Answer 25

You only add exponents when you multiply two powers with the same base.
For example, \(4^5 \times 4^7 = 4^{5 + 7} = 4^{12}\)

Answer 26

ahhh so it stays at 9a^2 ok that makes sense...so what are they talking about this fill in the blank thing in the second part? I still don't get that...

Answer 27

oh wait...no that part IS the fill in the blank part...the second part is the one where I have to rewrite it without exponents.

Answer 28

The second part is "blank a ^blank", right?

Answer 29

The second part is simply:

\(\large (3a)^2 = 9a^2\)

Answer 30

right the first part is the part where I have to write it without exponents.

Answer 31

For the first part, since you must write it without exponents, you must write the meaning of a^2 as a product.

What does a^2 mean as a product without using exponents?

Answer 32

a times a

Answer 33

Exactly.
That means,
\((3a)^2 = 3^2 a^2 = 9aa = 9 \times a \times a \)

Answer 34

so they just want me to give the equation...geez my class is weird

Answer 35

Maybe their idea is to make sure you understand what exponents mean.

Answer 36

(2z^2)^4 simplify without parentheses and my answer was 16z^8

Answer 37

Excellent.

Answer 38

really?!?!?

Answer 39

I got it?

Answer 40

I wouldn't say "Excellent, you're wrong." That would be mean.
I wrote Excellent to mean you did excellent work and are correct.

Answer 41

Yes, you got it.
I don't know why you're so surprised. You sound pretty smart to me.
You understood quickly the rule of exponents I showed you and applied it yourself correctly.

Answer 42

Sorry, I felt stunned...I'm usually so bad at getting this stuff...and my teacher this year has been very hard on me

Answer 43

Keep studying and asking questions. That's how you learn. I think you're on the right track.

Answer 44

(a^3/-3b)^2 write without parentheses a^6/9b^2

Answer 45

Correct & excellent, and don't be stunned.

Answer 46

I really have to thank you for helping me get my confidence :)

Answer 47

You are welcome.
Keep practicing and asking questions.

Answer 48

Ok I think I've almost got this one but I got a little stuck... find two consecutive whole numbers that sqrt65 lies in between and ummm so far I've got that 65 falls in the interval between 64 and 81 and it falls between 8 and 9 and then when I get the difference of 65 and 64 I get 1 and then I get the difference of 81 and 65 and I get 16...which is not 1/16 correct?...but now I'm stuck...

Answer 49

Yes, \(\sqrt{65} \) does lie between 8 and 9.