GCSE Maths Question regarding indices

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    Hi! Just need some help with questions like these

    (5x^1/2)^2
    (5x^2)^1/2

    I can do these types of questions with integers and negatives but not with halves. Any help much appreciated thanks!
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    (Original post by hhorse01)
    Hi! Just need some help with questions like these

    (5x^1/2)^2
    (5x^2)^1/2

    I can do these types of questions with integers and negatives but not with halves. Any help much appreciated thanks!
    You just need two rules: and \displaystyle (a^b)^c = a^{bc}.

    So, for example in your first question, you'd get: \displaystyle (5x^{1/2})^2 = 5^2 (x^{1/2})^2 = \displaystyle 25x^{\left(\frac{1}{2} \times 2 \right)} = 25x^1= 25x and you should be able to do the rest yourself.

    Remember that a^{1/2} = \sqrt{a}, so 5^{1/2} = \sqrt{5}.
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    (Original post by Zacken)
    You just need two rules: and \displaystyle (a^b)^c = a^{bc}.

    So, for example in your first question, you'd get: \displaystyle (5x^{1/2})^2 = 5^2 (x^{1/2})^2 = \displaystyle 25x^{\left(\frac{1}{2} \times 2 \right)} = 25x^1= 25x and you should be able to do the rest yourself.

    Remember that a^{1/2} = \sqrt{a}, so 5^{1/2} = \sqrt{5}.
    So the answer to the second would just be the square root of 5?

    What if the the integer power is not two?

    So (2x^3)^1/2
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    (Original post by hhorse01)
    So the answer to the second would just be the square root of 5?

    What if the the integer power is not two?

    So (2x^3)^1/2
    1. No. The second one is (5x^2)^{1/2}=\sqrt{5x^2}=\sqrt5 \cdot \sqrt{x^2} and finish it up from there.

    2. Then you do the same thing. (2x^3)^{1/2}=2^{1/2}\cdot (x^3)^{1/2}=\sqrt{2} \cdot x^{(3 \cdot \frac{1}{2})}=\sqrt{2} \cdot x^{3/2}
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    (Original post by RDKGames)
    1. No. The second one is (5x^2)^{1/2}=\sqrt{5x^2}=\sqrt5 \cdot \sqrt{x^2} and finish it up from there.

    2. Then you do the same thing. (2x^3)^{1/2}=2^{1/2}\cdot (x^3)^{1/2}=\sqrt{2} \cdot x^{(3 \cdot \frac{1}{2})}=\sqrt{2} \cdot x^{3/2}
    I'm really sorry but i still don't understand. Can you walk me through each one step by step?

    Wait no i get it now. Thanks a lot man!
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    (Original post by hhorse01)
    I'm really sorry but i still don't understand. Can you walk me through each one step by step?

    Wait no i get it now. Thanks a lot man!
    What would the actual answers be to those questions? The answers he got seemed to be just one number not two things multiplied.
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    (Original post by hhorse01)
    What would the actual answers be to those questions? The answers he got seemed to be just one number not two things multiplied.
    \sqrt{5}x
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    (Original post by hhorse01)
    What would the actual answers be to those questions? The answers he got seemed to be just one number not two things multiplied.
    Only one number? Then whoever got those answers is incorrect.

    Like for the first one: (5x^{1/2})^2=5^2(x^{1/2})^2=25(x)=25x
 
 
 
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