Talk:A-level Mathematics/OCR/C1/Indices and Surds

What do you do if the power isn't a rational number? For example, how is x to the power of root two defined?
 * The definition of irrational powers isn't required in C1, in fact I don't recall anywhere in A-Level Mathematics where it is formally taught. I can't remember the formal definition but $$x^{\sqrt{2}}$$ is the limit of $$x^1, x^{1.4}, x^{1.41}, x^{1.414}, x^{1.4142}\ldots$$.-- mattrix 21:30, 5 August 2005 (UTC)
 * Here's one formal definition: $$x^a = e^{\ln x^a} = e^{a\ln x}$$. That might not look any better but $$e^x$$ can be defined for any real $$x$$ without using irrational indices (for example, with the Maclaurin series, see Exponential_function). -- mattrix 21:43, 5 August 2005 (UTC)

rooth rule
The rule $$\sqrt{x\cdot y }=\sqrt{x}\cdot\sqrt{y}$$ only works if both x and y are non-negative, or one can easily "prove" that -1=1. Se http://en.wikipedia.org/wiki/Square_root

question
What if the indice is not 1/x to the power 3, but n/x to the power 3? what does the n do?

$$\frac{n^3}{x^3}$$ This is dictated by rule #6.Keytotime 20:23, 27 November 2006 (UTC)

Old introduction to indices.
I tried writing my own introduction as I found this one a little wordy.

You are probably already familiar with indices, for example $$x^2$$ is just a shorter way of writing $$x \times x$$ and $$x^4$$ is similarly $$x \times x \times x \times x$$. With $$x^5$$, $$x$$ is called the base and $$5$$ is called the power or exponent. $$x^4$$ is pronounced "x to the four", or "x raised to the 4th power" in full. Some powers are so useful that they have special names: $$x^2$$ is referred to as "x squared", $$x^3$$ is "x cubed" and $$x^{-1}$$ (which you will soon learn about if you haven't already encountered it) is called "the reciprocal of x".

Note: The "law of indices" is sometimes also called the "exponent laws" or "power rules". More generally, an index in mathematics is a superscript or subscript to a symbol.

Using this notation you might notice several patterns.

Conrad.Irwin 18:06, 29 November 2006 (UTC)

Division by Zero
Please be careful - x^4 / x is not x^3 if x is zero, as the division has undefined value. Simmilarly, x^2 times x^-1 is not x if x is zero, but rather is undefined for x^-1.

History???
i want to know who have founded these rules of indices??

Indices
Someone should solve this indices 8x-^3×3x^2/6x-^4 Thanks so much (discuss • contribs) 11:54, 31 January 2019 (UTC)