Simplify Expression 1

[harpazo]

Section R.2
Algebra Essentials
Michael Sullivan
Textbook: College Algebra Edition 9

Simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0.

See attachment for math work and answer. This is question 90.

 

[Deleted member 4993]

Section R.2
Algebra Essentials
Michael Sullivan
Textbook: College Algebra Edition 9

Simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0.

See attachment for math work and answer. This is question 90.

View attachment 13140

Correct....

 

[MarkFL]

[MATH]\frac{x^{-2}y}{xy^2}=x^{-2-1}y^{1-2}=x^{-3}y^{-1}=\frac{1}{x^3y}\quad\checkmark[/MATH]

 

[Otis]

… assume that the base is not 0 …

Hello. I'm not sure whether that's Sullivan's wording, but there are two bases in this exercise, so that instruction ought to reference both.

EG: Assume that neither base is zero or Assume all bases are non-zero.

Your work is fine. Mark showed a different way to view the simplification. Here's yet another, for your consideration (starting with your second step):

\[\frac{x^{-2}}{xy}\]

When we have a negative exponent in a ratio, we're allowed to move the power. (That's a shortcut.)

\[\frac{1}{x^{2} \cdot xy}\]

At this step, we see what the answer will be.

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