how does the negative sign work and/or where does it go?

[bobisaka]

how does the negative sign work and/or where does it go?

Does the negative sign go to the exponent or radical?

Note, I haven't actually used the negative sign in my solution,..

Simplify:

(81)^(-3/2)

1/(sqr 81)^3

1/(9)^3

1/729

 

[topsquark]

By definition (or you can prove it from another definition) [imath]a^{-b} \equiv \dfrac{1}{a^b}[/imath] so the negative sign implies a fraction, not anything to directly do with the exponent.

-Dan

 

[Dr.Peterson]

how does the negative sign work and/or where does it go?

Does the negative sign go to the exponent or radical?

Note, I haven't actually used the negative sign in my solution,..

Simplify:

(81)^(-3/2)

1/(sqr 81)^3

1/(9)^3

1/729

What you actually did here is to interpret the negative exponent immediately. If I were teaching this, I would have added an intermediate step or two:

(81)^(-3/2)​

​

1/(81)^{3/2) ... using a^-n = 1/a^n​

​

1/[(81)^(1/2)]^3 ... using a^(m/n) = a^[(1/n)*m] = [a^(1/n)]^m​

​

1/(sqrt(81))^3​

​

1/(9)^3​

​

1/729​

But your work is good.

 

[Otis]

… haven't actually used the negative sign in my solution…

(81)^(-3/2)
1/(sqr 81)^3

Actually, you have.

As Dan showed, the negation of an exponent indicates the reciprocal of the exponentiation.

You "used" the negative sign in your second step, where you changed from sqrt(81)^3 to the reciprocal of sqrt(81)^3.

Good job!

[imath]\;[/imath]