Thread: Simplify using Exponent Laws

I have two questions, if any help is given I'd appreciate it.

Simplify using the laws of exponents.

1) (3t - 2t^(-1)) / t^3

2) (3p^2 - p^(-3)) / p^4

Thank you very much.

Originally Posted by Jeavus

I have two questions, if any help is given I'd appreciate it.

Simplify using the laws of exponents.

1) (3t - 2t^(-1)) / t^3

Now simplify that.

The second question is done similarly

Can you explain how you got:

3 t^{1 - 3} - 2t^{-1-3}

Thanks.

EDIT: Nevermind, sorry.

Originally Posted by Jeavus

Can you explain how you got:

3 t^{1 - 3} - 2t^{-1-3}


Thanks.

There is a law of exponents that says

so, for instance, , since

So my final answers were:

(3t - 2t^(-1)) / t^3
= 3t / t^3 - 2t^(-1)/t^3
= 3t^(1-3) - 2t^(-1-3)
= 3t^(-2) - 2t^(-4)
= (3/t^2) - (2/t^4)
= (3t^2 - 2)/t^4

Is that correct?

(3p^2 - p^(-3))/p^4
= 3p^(2-4) - p^(-3-4)
= 3p^(-2) - p^(-7)
= (3/p^2) - (1/p^7)
= (3p^5 - 1) / p^7

Is that correct?

Originally Posted by Jeavus

So my final answers were:

(3t - 2t^(-1)) / t^3
= 3t / t^3 - 2t^(-1)/t^3
= 3t^(1-3) - 2t^(-1-3)
= 3t^(-2) - 2t^(-4)
= (3/t^2) - (2/t^4)
= (3t^2 - 2)/t^4

Is that correct?

(3p^2 - p^(-3))/p^4
= 3p^(2-4) - p^(-3-4)
= 3p^(-2) - p^(-7)
= (3/p^2) - (1/p^7)
= (3p^5 - 1) / p^7

Is that correct?

those don't really look simpler to me. you eliminated some of the variables, but the ones that remain have even higher powers than before. i would leave them separated as sums

How do I go about solving a problem like this?

1) (4 - (square root)x)/x^(3/2)

Originally Posted by Jeavus

How do I go about solving a problem like this?

1) (4 - (square root)x)/x^(3/2)

you do this the same as the last two, except you must know that

see post #3 here to learn how to change various root-forms into powers.

And do you know how to go abouts solving these two? Last two I promise.

1) (x-9) / (x^(1/2)-3)

2) (x-1)/((square root)x - x)

Originally Posted by Jeavus

And do you know how to go abouts solving these two? Last two I promise.

1) (x-9) / (x^(1/2)-3)

Notice that the top is the difference of two squares in terms of





Hopefully the last line is obvious to you

2) (x-1)/((square root)x - x)

Note that

how do you think you should proceed?

Hint: You do the same trick with the top as I did in the last question

Thanks so much for all your help.

PS: I did what you requested! :P

Originally Posted by Jeavus

Thanks so much for all your help.

PS: I did what you requested! :P

ok, just note that we have in the denominator, not , so you can't just cancel. more simplification is needed before you cancel anything