writing equation using indices

learning C1 atm and the text book doesnt really go into details about writing equation using indices -_-

why does 6/x² become 6x⁻²
and why does 3/2x^-1/2 become 3/2√4

(so sorry for the second one, im not familiar with making the -1/2 on computer :redface:

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Reply 1

Vikingninja

x^(-n) = 1/(x^n). The - in a power makes it the denominator. The number in front of the x values isn't affected because you are multiplying the function of x^-n by that value.

(edited 7 years ago)

Reply 2

TSR George

Here's the picture to make it more clear

Posted from TSR Mobile

Reply 3

Plagioclase

Well by definition

x^{-n} = \frac{1}{x^n}

, that's something you just have to learn. So

\frac{6}{x^2}=6 \times \frac{1}{x^2} = 6x^{-2}

. Using the exact same reasoning,

\frac{3}{2}x^{-\frac{1}{2}}=\frac{3}{2}\times \frac{1}{x^{\frac{1}{2}}} = \frac{3}{2} \times \frac{1}{\sqrt{x}} = \frac{3}{2\sqrt{x}}

Reply 4

RDKGames

Study Forum Helper

Original post by Plagioclase

Well by definition

x^{-n} = \frac{1}{x^n}

, that's something you just have to learn. So

\frac{6}{x^2}=6 \times \frac{1}{x^2} = 6x^{-2}

. Using the exact same reasoning,

\frac{3}{2}x^{-\frac{1}{2}}=\frac{3}{2}\times \frac{1}{x^{\frac{1}{2}}} = \frac{3}{2} \times \frac{1}{\sqrt{x}} = \frac{3}{2\sqrt{x}}

x*\frac{1}{x}=1

and similarly,

x*x^{-1}=x^1x^{-1}=x^{(1-1)}=x^0=1

therefore

x*\frac{1}{x}=x*x^{-1}

; divide both sides by x,

\frac{1}{x}=x^{-1}

Reply 5

TSR George

Original post by Vikingninja

x^(-n) = 1/(x^n). The - in a power makes it the denominator. The number in front of the x values isn't affected because you are multiplying the function of x^-n by that value.

Original post by Plagioclase

Well by definition

x^{-n} = \frac{1}{x^n}

, that's something you just have to learn. So

\frac{6}{x^2}=6 \times \frac{1}{x^2} = 6x^{-2}

. Using the exact same reasoning,

\frac{3}{2}x^{-\frac{1}{2}}

=\frac{3}{2}\times \frac{1}{x^{\frac{1}{2}}} = \frac{3}{2} \times \frac{1}{\sqrt{x}} = \frac{3}{2\sqrt{x}}

thanks, i stared at this for 5 minutes and finally got it :redface:

would u say 3/2x ^ -1/2 is the hardest i'll get?

(edited 7 years ago)

Reply 6

Vikingninja

It'll be harder in exams but you will have a while to practice it. You can get stuff like -4/3.

Reply 7

TSR George

Original post by Vikingninja

It'll be harder in exams but you will have a while to practice it. You can get stuff like -4/3.

to the power of -4/3?

so i would cube root it and raise it to power of 4 but only for x, not the number before it as it's unaffected by the power? am i right? :redface:

Reply 8

Plagioclase

No, but these things will get a lot easier over time as you get used to them :smile:

Reply 9

TSR George

Original post by Plagioclase

No, but these things will get a lot easier over time as you get used to them :smile:

how do you remember it? do you write notes about little things like this or do you just do questions on it to let it sink in? i feel like i shouldnt study maths like i would with history with tons of notes and stuff

Reply 10

RDKGames

Study Forum Helper

Well first you would flip it to be 1 over that number raised to the 4/3 (we call this to be the reciprocal). Then you cube root that number while raising it to the 4th power.

Alternatively, after you take the reciprocal, you can split the 4/3 into 1+1/3 and think of that power as a sum, hence you can separate the variable using laws of indices.

(edited 7 years ago)

Reply 11

RDKGames

Study Forum Helper

You will do loads of questions. Practice makes perfect. After GCSE maths and 2 A-Level maths subjects, I can safely say I never looked back on my books in terms of notes unless it is a subject I'm really not confident on. You just practice loads of questions and it sinks in.

Reply 12

TSR George

Original post by RDKGames

that made more sense to me :hoppy:

Reply 13

Vikingninja

You would put it as the denominator first so then its to the power of 4/3, then get the value to the power of 4 and then cube root that. You won't necessarily have to always find a value of x to a power with this stuff.