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a. (-2.5)^3/(-2.5)^-2

 

b. (3^3)(3^-6)

 

c. s^2 t^-1/(s^4 t^4)^1/2

 Aug 9, 2017
 #1
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A.(-2.5)^3/(-2.5)^-2

Intepretation: \(\frac{\left(-2.5\right)^3}{\left(-2.5\right)^{-2}}\)

The negative second power will be positive, for the third power it is negative.

Rewrite as:\(-\frac{\left(2.5\right)^3}{\left(2.5\right)^{-2}}\)

\(=-\left(2.5\right)^5\)

\(=-97.65625\)

B.(3^3)(3^-6)

Intepretation: \(\frac{3^3}{3^{-6}}\)

\(=3^9\)

\(=19,683\)

C.s^2 t^-1/(s^4 t^4)^1/2

Intepretation: \(\frac{s^2t^{-1}}{\left(s^4t^4\right)^{\frac{1}{2}}}\)

\(=\frac{s^2t^{-1}}{s^2t^2}\)

The \(s^2\) cancels each other out:

\(=\frac{t^{-1}}{t^2}\)

\(=t^{-3}\)

Q.E.D.

 Aug 9, 2017

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