Hey there! Sign in to join this conversationNew here? Join for free

Power Question C1 Watch

Announcements
    • Thread Starter
    Offline

    0
    ReputationRep:
    x^{3/2} = 1 , 8

    To get x , do I do root 8 then power it by 3 ? , Or do I do cube root 8 then power it by 2 ?

    I'm not sure if the sign get flipped when it moves to the other side ?
    Offline

    0
    ReputationRep:
    the number at the bottom falls down and rises up again as a power, so it is root x ^ 3.

    so x = 4
    Offline

    2
    ReputationRep:
    x^{\frac{3}{2}} = 8

    is the same as saying

    1. (x^\frac{1}{2})^3 = 8

    and it is also the same as saying

    2. (x^3)^{\frac{1}{2}} = 8

    ^ due to indice rules involving multiplication. You'll see that multiplying the indices together in each equation gives you the same power of x.

    ---------------

    A good thing to remember:

    x^{\frac{1}{2}}=\sqrt{x}

    ---------------



    To solve for x in (1):

    (x^\frac{1}{2})^3 = 8

    x^{\frac{1}{2}}=\sqrt[3]{8} = 2, to get rid of the outside power of 3.

    x= 2^2 = 4. Anything to the power of 1/2 is the same as using a square root sign. To get rid of square roots, we square both sides.

    ---------------



    To solve for x in (2):

    (x^3)^{\frac{1}{2}} = 8
    x^3 = 8^2 for the same reason as above.

    x=\sqrt[3]{64}=4 because "cube root" "undoes" "to the power of 3"


    ---------------


    Just for your knowledge, you can always test your method by working backwards and seeing if you get to the beginning again.

    To get x , do I do root 8 then power it by 3 ?

    Let's test it out:

    x=(\sqrt{8})^3, because you're powering the whole of "root 8" by 3 (so you can put it in brackets like so)

    \sqrt[3]{x}=(\sqrt{8})

    (x^\frac{1}{3})^2=8

    = x^\frac{2}{3} - this is clearly not equivalent to the first bit
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Will you be richer or poorer than your parents?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.