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December 20, 2014

December 20, 2014

Posted by **Zava** on Monday, October 26, 2009 at 6:48pm.

How do you write a fractions an expression using a negative exponent?

- Math -
**jim**, Monday, October 26, 2009 at 7:43pmI'll try to answer the case I think you're asking about. If I'm guessing wrong, do ask again.

If you have something like x^2 * x^3 (x-squared times x-cubed) then you add the exponents:

x^2 * x^3 = x^5

Similarly, in general,

x^a * x^b = x^(a+b)

With negative exponents, you drop the negative bit, and write "one over" the expression, thus:

x^(-1) = 1/x

x^(-2) = 1/x^2

x^(-3.14159) = 1/x^3.14159

and in general

x^(-a) = 1/x^a

- Math -
**Zava**, Monday, October 26, 2009 at 7:57pmlike, the scientific notation?

- Math -
**jim**, Monday, October 26, 2009 at 8:00pmYes, but "scientific notation" is often used when talking about powers of 10, like:

20000 = 2 * 10^4

This makes arithmetic with large numbers easy, since, following the rule above, all you have to do is add powers to multiply the factors of 10, like:

(2.1 * 10^5) * (3 * 10^4)

= 2.1 * 3 * 10^5 * 10^4

= 6.1 * 10^9

- Math -
**jim**, Monday, October 26, 2009 at 8:01pmOops: that last line should have been

= 6.3 * 10^9

of course!

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