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    I can't seem to comprehend this.

    If y = 2^x, then 4^x will surely by 2*y, to get 2 * 2^x = 4^x.

    Yet the answer seems to be y^2. Why is that? Wouldn't 2^x * 2^x = 4^2x, not 4^x ?
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    (Original post by frostyy)
    I can't seem to comprehend this.

    If y = 2^x, then 4^x will surely by 2*y, to get 2 * 2^x = 4^x.

    Yet the answer seems to be y^2. Why is that? Wouldn't 2^x * 2^x = 4^2x, not 4^x ?
    You seem to think that 2 \times 2^5 = 4^5. That is not true. Instead, we have 2 \times 2^5 = 2^6. Check it with your calculator.

    In general: 2 \times 2^x = 2^{x+1} \neq 4^{x}. This obeys the indices law a^x \times a^y = a^{x+y} (note that the bases have to be the same).

    However, (a^x)^y = a^{xy}. So a^{2x} = (a^{x})^2.
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    (Original post by frostyy)
    I can't seem to comprehend this.

    If y = 2^x, then 4^x will surely by 2*y, to get 2 * 2^x = 4^x.

    Yet the answer seems to be y^2. Why is that? Wouldn't 2^x * 2^x = 4^2x, not 4^x ?
    You are getting your rules of indices wrong.

    When we multiply, we add the indices. e.g. 2^a \times 2^b = 2^{a+b}

    When we raise to a power, we multiply the indices, e.g. (2^x)^2 = 2^{2x}

    Hence returning to your example, 2y = 2 \times 2^x = 2^{x+1} which is not the same as 4^x
    Meanwhile, y^2 = (2^x)^2 = 2^{(2x)} = (2^2)^x = 4^x

    Edit: Too slow...
    Second edit: And a LaTeX error...
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    when you multiply you add the powers so,
    \left (2  \right )2^{x} = 2^{x+1}

    Multiply when a power is raised to another power
    (2^{x})^{2} = 2^{2x}=(2^{2})^{x}=4^{x}
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    (Original post by frostyy)
    ...
    If it helps, you may want to think of 2^x as \displaystyle \underbrace{2 \times 2 \times \cdots \times 2}_{x \, \text{times}}

    So if you multiply it by 2: \displaystyle 2 \times 2^{x} = 2 \times \underbrace{2 \times 2 \times \cdots \times 2}_{x \, \text{times}} = \underbrace{2 \times 2 \times \cdots \times 2}_{(x+1) \, \text{times}} = 2^{x+1} \neq 4^x.

    That's the way I teach it to my students.
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    (Original post by Zacken)
    If it helps, you may want to think of 2^x as \displaystyle \underbrace{2 \times 2 \times \cdots \times 2}_{x \, \text{times}}

    So if you multiply it by 2: \displaystyle 2 \times 2^{x} = 2 \times \underbrace{2 \times 2 \times \cdots \times 2}_{x \, \text{times}} = \underbrace{2 \times 2 \times \cdots \times 2}_{(x+1) \, \text{times}} = 2^{x+1} \neq 4^x.

    That's the way I teach it to my students.
    Okay, thank you, I understand why I was wrong in the first place.

    Yet I still fail to get this:

    Surely, it'd be 2^x + x, according to the rules of indices?
    how is 2^x * 2^x = 4^x? Does this mean that 4^x is the same as 2^2x?
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    (Original post by frostyy)
    ...
    Indeed, it does. Have you heard of the rule that (a^x)^y = a^{xy} = (a^y)^x.

    So 2^x \times 2^x = 2^{2x} = (2^{2})^x = 4^x.
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    (Original post by Zacken)
    Indeed, it does. Have you heard of the rule that (a^x)^y = a^{xy} = (a^y)^x.

    So 2^x \times 2^x = 2^{2x} = (2^{2})^x = 4^x.
    Thank you. I never expected a 1 marker to show me this many holes in my logic and knowledge (perhaps intelligence too as of being unable to see the links ;p).

    Cheers
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    (Original post by frostyy)
    Thank you. I never expected a 1 marker to show me this many holes in my logic and knowledge (perhaps intelligence too as of being unable to see the links ;p).

    Cheers
    It's good that it has, now you know that you can work on them. It might be useful googling "indices laws" and refreshing your memory.
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    (Original post by Zacken)
    If it helps, you may want to think of 2^x as \displaystyle \underbrace{2 \times 2 \times \cdots \times 2}_{x \, \text{times}}

    So if you multiply it by 2: \displaystyle 2 \times 2^{x} = 2 \times \underbrace{2 \times 2 \times \cdots \times 2}_{x \, \text{times}} = \underbrace{2 \times 2 \times \cdots \times 2}_{(x+1) \, \text{times}} = 2^{x+1} \neq 4^x.

    That's the way I teach it to my students.
    You're a teacher?
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    (Original post by Serine Soul)
    You're a teacher?
    I tutor a bunch of year 9's thrice a week, helps stave off the boredom that sets in when you don't go to school. :lol:
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    (Original post by Zacken)
    I tutor a bunch of year 9's thrice a week, helps stave off the boredom that sets in when you don't go to school. :lol:
    Ah I see

    Do you give them stickers if they're good? :teehee:
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    (Original post by Serine Soul)
    Ah I see

    Do you give them stickers if they're good? :teehee:
    That's a fantastic idea, I wonder if that's what Cambz supervisors do. :teehee:
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    (Original post by Serine Soul)
    Ah I see

    Do you give them stickers if they're good? :teehee:
    I bet he gives them lashes with his cane
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    (Original post by Student403)
    I bet he gives them lashes with his cane
    :shakecane:
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    (Original post by Zacken)
    :shakecane:
    :rofl: PRSOM
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    (Original post by Zacken)
    That's a fantastic idea, I wonder if that's what Cambz supervisors do. :teehee:
    With only the finest :mmm:

    Name:  X7_1_Zoom.jpg
Views: 509
Size:  214.9 KB

    (Original post by Student403)
    I bet he gives them lashes with his cane
    Not. *whack* STEP. *whack* Standard. *whack*
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    (Original post by Serine Soul)
    With only the finest :mmm:

    Name:  X7_1_Zoom.jpg
Views: 509
Size:  214.9 KB


    Not. *whack* STEP. *whack* Standard. *whack*
    XD
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    (Original post by Zacken)
    That's a fantastic idea, I wonder if that's what Cambz supervisors do. :teehee:
    In my experience, they just didn't glare at you if you got something right.
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    (Original post by Gregorius)
    In my experience, they just didn't glare at you if you get something right.
    Can't wait to not be glared at, sounds like a real treat. :lol:
 
 
 
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