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Math Help - Simplify the following indices

  1. #1
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    Simplify the following indices

    Firstly, I am quite new to indices in mathematics, though I am not sure about using fractions when it comes to pronumerals as well. So, any help is appreciated.

    Simplify the following questions:

    1. p^6q^4 divided by p^q
    2. 8w^10 divided by 2w^4
    3. 2x^6 multiplied by 5x, divided by 10x^4
    4. (2g^2)^2
    5. 20d^8e^6 divided by 2d^2e multiplied by 5d^2e^2

    Thank you for your time. I shall be waiting!
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    Quote Originally Posted by JadeKiara View Post
    Firstly, I am quite new to indices in mathematics, though I am not sure about using fractions when it comes to pronumerals as well. So, any help is appreciated.

    Simplify the following questions:

    1. p^6q^4 divided by p^q
    2. 8w^10 divided by 2w^4
    3. 2x^6 multiplied by 5x, divided by 10x^4
    4. (2g^2)^2
    5. 20d^8e^6 divided by 2d^2e multiplied by 5d^2e^2

    Thank you for your time. I shall be waiting!
    Here are the rules you need to know:

    (1) x^a \cdot x^b = x^{a + b}

    (2) \frac {x^a}{x^b} = x^{a - b}

    (3) (x^a)^b = x^{ab}

    (4) (xy)^a = x^a y^a

    now, try the problems, you can work on them one at a time and check back here
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    Hmmm... I don't quite understand

    Yes, I have tried a few times at these and with no success. I have several scrunches of paper strewn around me and I am still failing miserably. Please help me and explain the process in which to solve these!
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    Quote Originally Posted by JadeKiara View Post
    Yes, I have tried a few times at these and with no success. I have several scrunches of paper strewn around me and I am still failing miserably. Please help me and explain the process in which to solve these!
    i told you everything you need to know, just follow the rules

    for example, the first

    \frac {p^6q^4}{p^q} = \frac {p^6}{p^q}q^4 = p^{6 - q}q^4 ....by rule (2)

    ...by the way, are you sure it should be p^{\color{red}q}
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    remember the rules:

    *in dividing polynomials just subtract the exponent the divisor from the exponent of the dividend

    *in multiplying say for example (2x^2)(3x^3) just add the

    exponents 6x^5

    * when a polynomial like (2x^2)^2 you just get the

    square of to then multiply the exponent that is 2 with

    2.
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    I will try again, and by the way, it was not pq. It was a typing error, so it should be p^6 q^4 divided by p^3 q....
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    Quote Originally Posted by JadeKiara View Post
    I will try again, and by the way, it was not pq. It was a typing error, so it should be p^6 q^4 divided by p^3 q....
    that's a huge typo, but anyway


    \frac {p^6q^4}{p^3q} = \frac {p^6}{p^3} \cdot  \frac {q^4}q = p^{6 - 3} q^{4 - 1} = p^3q^3 = (pq)^3

    do you see how the rules were applied?
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    Ah, I see what you mean (it was due to my huge typo). Would you like me to post my answers soon or is that all?
    I have thanked you by the way Jhevon.
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    Quote Originally Posted by JadeKiara View Post
    Ah, I see what you mean (it was due to my huge typo). Would you like me to post my answers soon or is that all?
    I have thanked you by the way Jhevon.
    post your answers whenever (hopefully before they are due ), we will check them

    thanks for the thanks
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    You are most welcome. Sorry about the typo before, I am new to notation on the computer. I don't have much time, so please be as fast as possible, in half an hour I have to leave (it is due tomorrow morning!!! ).

    I have tried my best, and correct me if I am wrong:

    1. p^6q^4 divided by p^q
    = (pq) ^3

    2. 8w^10 divided by 2w^4
    = w^12

    3. 2x^6 multiplied by 5x, divided by 10x^4
    = 13x / 14x

    4. (2g^2)^2
    = 2g^4 OR g^6 ???

    5. 20d^8e^6 divided by 2d^2e multiplied by 5d^2e^2
    = d^17 X e^4


    I have written down the rules as well to help me in future.
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    Quote Originally Posted by JadeKiara View Post
    You are most welcome. Sorry about the typo before, I am new to notation on the computer. I don't have much time, so please be as fast as possible, in half an hour I have to leave (it is due tomorrow morning!!! ).

    I have tried my best, and correct me if I am wrong:

    1. p^6q^4 divided by p^q
    = (pq) ^3
    you did the same typo again

    2. 8w^10 divided by 2w^4
    = w^12
    no

    note that you have \frac 82 \cdot \frac {w^{10}}{w^4}

    3. 2x^6 multiplied by 5x, divided by 10x^4
    = 13x / 14x
    no, you have \frac {2 (5)}{10} \cdot \frac {x^6 \cdot x}{x^4}


    4. (2g^2)^2
    = 2g^4 OR g^6 ???
    no. princess21 warned you about this also: (2g^2)^2 = 2^2 \cdot (g^2)^2 now finish up


    5. 20d^8e^6 divided by 2d^2e multiplied by 5d^2e^2
    = d^17 X e^4
    again, no (are you sure you are seeing how to apply the rules?)

    i suppose you mean \frac {20d^8e^6}{2d^2e} \cdot 5d^2e^2

    you have: \frac {20(5)}2 \cdot \frac {d^8 \cdot d^2}{d^2} \cdot \frac {e^6 \cdot e^2}e
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    Ah, I know, I am terrible at maths. Did you provide the answer under the explanation? I don't yet understand experienced terms like 'polynomial' but I am working on it. I just really need help with this, as it was given as homework and we have never done indices before. The teacher said we had to find out by ourselves.
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    Quote Originally Posted by JadeKiara View Post
    Ah, I know, I am terrible at maths.
    stop saying that and start trying harder. everything is difficult the first time. learning your ABCs was hard once upon a time.

    Did you provide the answer under the explanation?
    i only answered the first one completely. the others you have to finish. i put each in a form where you can apply the rules easily. do you see how i got to these forms? try the problems again

    I don't yet understand experienced terms like 'polynomial' but I am working on it.
    don't worry about that yet. knowledge of polynomials is not needed here, just follow the rules.

    I just really need help with this, as it was given as homework and we have never done indices before. The teacher said we had to find out by ourselves.
    you found it. i told you all you need to know. you are no longer in the dark. just try to pay attention and see where you can apply the rules.
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    Sorry for complaining. I'm just a bit stressed. I have been doing maths all day and I have hit an obstacle I can't seem to get past. Do the rules have to be applied in every problem (that's what I do not understand)?

    For example:

    I don't know how the 8 works or the 2. Can you add it to the indices?

    8w^10
    ------- =
    2w^4
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    Quote Originally Posted by JadeKiara View Post
    Sorry for complaining. I'm just a bit stressed. I have been doing maths all day and I have hit an obstacle I can't seem to get past. Do the rules have to be applied in every problem (that's what I do not understand)?

    For example:

    I don't know how the 8 works or the 2. Can you add it to the indices?

    8w^10
    ------- =
    2w^4
    yes, you would apply the rules here for w. as far as the 8/2 is concerned, that's just 4

    you separate each kind of term as you saw me do, and simplify each. so think of the 8/2 separate and then you have the (w^10)/(w^4). work out each separately, and then multiply them together when done
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