## anonymous 5 years ago Can anyone solve this insanity of Simplifying Exponent Expressions?????? Its (-3x^-1 y^-2)(2x^4 y^-3) ???????????/

1. anonymous

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

2. anonymous

$-6x^{-1+4}y^{-2-3}$

3. anonymous

But it says to write it as positive exponents

4. Hero

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

5. 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.

6. 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 $\frac{-6x^3}{y^5}$

7. anonymous

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

8. anonymous

Thanks...

9. Hero

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

10. anonymous

Can I throw another 1 @ ya?

11. 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).