Question

someone please help me on simplifying expressions!

Answer 1

Do I need to make an example, or do you need help with a question?

Answer 2

it's questions, but I did some trying to use the methods you showed me but I get stuck :/

Answer 3

Okay

Answer 4

For your first one:

Answer 5

Be aware that the topic here is "exponentiation" and that you're being asked to simplify expressions with exponents.

Answer 6

yes, I'm sorry.

Answer 7

For Problem #59: Imagine you had (a/b)^(-1). How would you evaluate that?

Answer 8

In nicer format, that'd be \[(\frac{ a }{ b })^{-1}\]

Answer 9

do the reciprocal since it has a negative exponent? :/

Answer 10

Yes. Go ahead: try it.

Answer 11

1/ (a/b) ?

Answer 12

That's correct, but it'd be much easier simply to write b/a, don't you think?

Answer 13

\[(a/b)^{-1}=b/a\]

Answer 14

may I ask why b/a is easier than a/b because I'm kind of confused :/ ?

Answer 15

(2x^3 y^4)^5

2^5x^15 y^20

(32x^15 y^20)

\[32x^15 y^20\]

Answer 16

thats question 68
and the last one is supposed to be

32^15 y^20

Answer 17

What I actually said was that your (correct)\[\frac{ 1 }{ a/b }\]is more simply expressed as b/a.
I inverted (a/b) to obtain (b/a).

Answer 18

Simplify the following:
\[x^2/(1/(x^3 y^2)) \]\[ x^2/(1/(x^3 y^2)) \]as a single fraction.
Multiply the numerator of
\[ \frac{x^2}{\frac{1}}{\frac{x^3 y^2}}\] by the reciprocal of the denominator.
\[ \frac{x^2}{\frac{1}{x^3 y^2}} = x^2 x^3 y^2: \]\[x^2 x^3 y^2 \]Combine products of like terms.
\[x^2 x^3 y^2 = x^{2+3} y^2:\]\[x^{2+3} y^2\]Evaluate 2+3.
\[2+3 = 5: \]God, it's so hard to type fractions on fractions, sorry -.-

Answer 19

Oops that was a waste of time.

Answer 20

Too many helpers here, I'm afraid. Which one of us is going to bow out?

Answer 21

That'll be me, I helped her enough earlier :P

Answer 22

Sweet of you. Apparently you're not as dangerous as your name implies.

Answer 23

dominiquebee72 where's the 32 from..?

Answer 24

thank you all for helping, I appreciate it, if I haven't replied it's because i'm going over it :)

Answer 25

Here you see the danger in providing answers without explanations and without involving the person asking the question. Please, @dominiquebee72, help @heyitslizzy13 to find her own answers by providing her with guidance along the way.

Answer 26

thanks @mathmale I don't even know which problem to look at I'm so confused .-.

Answer 27

@heyitslizzy13 : Please look at Problem #59:\[(\frac{ x^2 }{ x ^{-3}y ^{-2} })^{-1}\]and then apply what I was demonstrating earlier. In other words, simply flip the quantity within the parentheses.

Answer 28

so x^3 y^2 / x^2 ?

Answer 29

@DangerousJesse thanks a lot for your help!! :)

Answer 30

If we invert the quantity inside parentheses, we'd get \[\frac{ x ^{-3}y ^{-2} }{ x^2 }\]... note that the exponent is now gone.

Answer 31

What's the last thing you'd do to simplify this? Remember, we don't want negative exponents.

Answer 32

wait what happened to the exponent on the outisde..? I thought the exponents would then be positive since we did the reciprocal ?

Answer 33

There was a negative 1 exponent. We got rid of that simply by inverting / flipping the quantity within the parentheses.

Answer 34

Or, as you say, we found the reciprocal of the original quantity within parentheses.

Answer 35

oh sorry, I thought you had to apply the -1 exponent to the numbers inside the parentheses

Answer 36

You certainly can do EITHER that OR flip the original quantity within parentheses. I chose to do the latter.

Answer 37

So, going back to \[\frac{ x ^{-3}y ^{-2} }{ x^2 }\]how are you going to eliminate those negative exponents?

Answer 38

reciprocal again?

Answer 39

That would work. What i'd suggest, however, is that you recognize that that \[x ^{-3}\]in the numerator becomes x^3 in the denominator. Can you agree with that?

if so, what is (x^3)(x^2)?

Answer 40

x^5?

Answer 41

Yes. So your newest and last denominator is x^5. What happens to that \[y ^{-2}\]in the numerator?

Answer 42

Hint: re-write \[y ^{-2}\] with positive exponent.

Answer 43

y^2 / x^5 ?

Answer 44

i'm still not sure how I even got there .-.

Answer 45

that \[y ^{-2}\] becomes \[\frac{ 1 }{ y^2 }\]so,

Answer 46

\[\frac{ y ^{-2} }{ x^2 }\] becomes what?

Answer 47

sorry, I meant\[\frac{ y ^{-2} }{ x^5 }\]

Answer 48

x^5 / y^2 ?