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GCSE Maths Question regarding indices

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!
Reply 1
Avatar for Zacken
Zacken
22
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: [tex(ab)^c - a^c b^c] and (ab)c=abc\displaystyle (a^b)^c = a^{bc}.

So, for example in your first question, you'd get: (5x1/2)2=52(x1/2)2=25x(12×2)=25x1=25x\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. :smile:

Remember that a1/2=aa^{1/2} = \sqrt{a}, so 51/2=55^{1/2} = \sqrt{5}.
(edited 7 years ago)
Reply 2
Avatar for james02jjk
james02jjk
OP
7
Original post by Zacken
You just need two rules: [tex(ab)^c - a^c b^c]
and (ab)c=abc\displaystyle (a^b)^c = a^{bc}.

So, for example in your first question, you'd get: (5x1/2)2=52(x1/2)2=25x(12×2)=25x1=25x\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. :smile:

Remember that a1/2=aa^{1/2} = \sqrt{a}, so 51/2=55^{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
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 (5x2)1/2=5x2=5⋅x2(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. (2x3)1/2=21/2⋅(x3)1/2=2⋅x(3⋅12)=2⋅x3/2(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}
(edited 7 years ago)
Reply 4
Avatar for james02jjk
james02jjk
OP
7
Original post by RDKGames
1. No. The second one is (5x2)1/2=5x2=5⋅x2(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. (2x3)1/2=21/2⋅(x3)1/2=2⋅x(3⋅12)=2⋅x3/2(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!
(edited 7 years ago)
Reply 5
Avatar for james02jjk
james02jjk
OP
7
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.
Reply 6
Avatar for Zacken
Zacken
22
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.


5x\sqrt{5}x
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: (5x1/2)2=52(x1/2)2=25(x)=25x(5x^{1/2})^2=5^2(x^{1/2})^2=25(x)=25x

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