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March 27, 2017

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How do you simplify a expression with positive exponents?

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

  • Math - ,

    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

  • Math - ,

    like, the scientific notation?

  • Math - ,

    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

  • Math - ,

    Oops: that last line should have been

    = 6.3 * 10^9

    of course!

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