# Thread: I need help

1. ## I need help

Any help would be greatly appreciated. Thanks.

2. Hi

$\displaystyle \frac{10\:x^{-2}:y^3\cdot\:5^{-1}\:\frac{1}{y}}{\frac{1}{x^2}\:2\:\frac{1}{y^4}} = \frac{10}{x^2}\:\frac{1}{y^3}\:\frac{1}{5}\:\frac{ 1}{y}\:x^2\:\frac{1}{2}\:y^4 = 1$

3. Originally Posted by running-gag
Hi

$\displaystyle \frac{10\:x^{-2}:y^3\cdot\:5^{-1}\:\frac{1}{y}}{\frac{1}{x^2}\:2\:\frac{1}{y^4}} = \frac{10}{x^2}\:\frac{1}{y^3}\:\frac{1}{5}\:\frac{ 1}{y}\:x^2\:\frac{1}{2}\:y^4 = 1$
Should it be $\displaystyle y^6$ instead of 1? (I'm assuming the semi-colon as a typo for multiplication)

For Q2,

use this rule:
log (a) + log (b) = log (a*b)
log (a) - log (b) = log (a/b)

And you will transform the line into a fraction to simplify.

4. Originally Posted by knighty
Should it be $\displaystyle y^6$ instead of 1? (I'm assuming the semi-colon as a typo for multiplication)
You may be right
I assumed ":" was a division

5. Your images are somewhat huge, so I'll repost the exercises here, along with my guesses as to what the instructions had been.

$\displaystyle \mbox{1) Simplify: }\, \frac{\left(10x^{-2}\right)(y^3)(5^{-1})\left(\frac{1}{y}\right)}{\left(\frac{1}{x^2}\r ight)\left(2\right)\left(\frac{1}{y^4}\right)}$
To learn the rules for exponents, try here. To learn how to simplify expressions such as the above, try here.

To get you started:

. . . . .$\displaystyle \frac{\left(\frac{10}{x^2}\right)\left(\frac{y^3}{ 1}\right)\left(\frac{1}{5}\right)\left(\frac{1}{y^ 1}\right)}{\left(\frac{1}{x^2}\right)\left(\frac{2 }{1}\right)\left(\frac{1}{y^4}\right)}\, =\, \frac{\left(\frac{10\times y^3\times 1 \times 1}{x^2\times 1\times 5\times y}\right)}{\left(\frac{1\times 2\times 1}{x^2 \times 1\times y^4}\right)}\, =\, \left(\frac{10y^3}{5x^2 y}\right)\, \times\, \left(\frac{x^2 y^4}{2}\right)$

$\displaystyle \mbox{2) Combine into one term: }\, \log(20b^3)\, -\,\log(5^2 b^2)\, +\, log(35)\, -\, log(28)$
To learn what the rules are and how to use them, try here.

To get you started:

. . . . .$\displaystyle \log(20b^3)\, -\,\log(5^2 b^2)\, +\, log(35)\, -\, log(28)$

. . . . .$\displaystyle =\, \log(20b^3)\, +\, \log(35)\, -\, \left(\log(5^2 b^2)\, +\, \log(28)\right)$

. . . . .$\displaystyle =\, \log\left(20b^3\, \times\, 35\right)\, -\, \log\left(5^2 b^2\, \times \, 28\right)$

$\displaystyle \mbox{3) Given }\, P(x)\, =\, 5x^3\, -\,4x^2\, +\,2x \, -\, 1\, \mbox{ and }\, D(x)\, =\, x\, -\, 2,$

$\displaystyle \mbox{find the product }\, \left(P(x)\right)\left(D(x)\right).$
To learn how to multiply polynomials, try here.

Once you have learned the basic terms and techniques, please attempt the exercises. If you get stuck, you will then be able to reply with a clear listing of your work and reasoning so far, so we can "see" where you're stuck and then provide intelligent assistance.

Thank you!

6. Thanks a lot for the tips and the link, great side.