Can't figure out how to solve this!

Otis

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Apr 22, 2015
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positive leading coefficient for the exponent ... and vice versa
I hope that I'm not misunderstanding, but it seems the description above works only for the specific form in this exercise -- assuming n itself is a Whole number.

When I read 'leading coefficient', then for a negative case (in general), I think of

a^(-n + b)

That exponent has a negative leading coefficient, yet we can't say whether the expression represents a power of 'a' or the reciprocal of that power.

:)
 

Otis

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Joined
Apr 22, 2015
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3,682
Hi snakehead. Here's the definition used for the final simplification.

a^(-n) = 1/a^n

In other words, if you see a negated exponent, you may immediately consider the reciprocal of the power.

😎
 

Otis

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Apr 22, 2015
Messages
3,682
The following may be off-topic, but I'd like to share an alternate simplification.

There are many ways to "simplify" algebraic expressions. Expressions in beginning courses are often cooked up for practicing specific definitions, properties and/or rules.

Later on, when we use our skills to algebraically manipulate given information, there might be a specific goal in mind concerning a specific application in the real world.

For example, later on we might be working with exponential growth over time (of some chemical reaction, perhaps), using a model like this:

y = a*b^t

Let's say the expression given in this thread is an example of some potential data from chemistry experiments. We may simplify it to obtain the exponential form above (treating n as the time variable).

y = (9/125)*(3/125)^n

a = 9/125
b = 3/125
t = n

This alternate simplification can be obtained by applying definitions and proprties, just like the OP did, but with a different goal in mind.

😎
 
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