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Mathematics
OpenStudy (anonymous):

Can anyone solve this insanity of Simplifying Exponent Expressions?????? Its (-3x^-1 y^-2)(2x^4 y^-3) ???????????/

OpenStudy (anonymous):

\[(-3x^{-1} y^{-2})(2x^4 y^{-3}) \] it is just bookkeeping. add the exponents

OpenStudy (anonymous):

\[-6x^{-1+4}y^{-2-3}\]

OpenStudy (anonymous):

But it says to write it as positive exponents

hero (hero):

I personally hate negative exponents. You'll never see a negative exponent in any of my solutions.

OpenStudy (anonymous):

ok satellite has already done all the hard work, the rest is easy if you wish to write it in terms of positive exponents.

OpenStudy (anonymous):

Here is what Satellite got to: \[-6x^{3}y^{-5}\] then you know that a negative exponent means a fraction - i.e. \[a^{-b} = \frac{1}{a^b}\] so we have \[\frac{-6x^3}{y^5}\]

OpenStudy (anonymous):

when multiplying, add the indices, when raising to the power multiply the indices...

OpenStudy (anonymous):

Thanks...

hero (hero):

negative exponent actually means means "inverse". so a^-b really means inverse of a^b which equals 1/a^b

OpenStudy (anonymous):

Can I throw another 1 @ ya?

OpenStudy (anonymous):

yeah, it's the multiplicative inverse isn't it: a^(b) has multiplicative inverse a^(-b). In the real number field this is equal to 1/a^b. However, in groups for example, there's no concept of a number so we stick to a^(-1) as the inverse of a. Since we are in the real numbers, a^b has inverse a^(-b).

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