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# simplify this expression, do not evaluate?

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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

Guest Aug 9, 2017
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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.

Jeffes02  Aug 9, 2017

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