posted by Zava on .
How do you simplify a expression with positive exponents?
How do you write a fractions an expression using a negative exponent?
I'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
like, the scientific notation?
Yes, 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
Oops: that last line should have been
= 6.3 * 10^9