Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Negative Exponents

Let a = any number = n.

Prove that a^(-n) = 1/ a^(n), where a does not equal 0.

Why must we put a^(n) under 1?

Where does 1 come from?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Negative Exponents

Read the (number)^1 and a^0 answers first.

Using rule one  a^n x a^(-n) = a^(n-n) = a^0 = 1

So a^(-n) behaves like 1/(a^n) so it is defined to be that.

Other properties involving powers can be 'worked out' using the rules.

eg.  You can work out what a^(0.5) means by considering a^(0.5) x a^(0.5)

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Negative Exponents

Read the (number)^1 and a^0 answers first.

Using rule one  a^n x a^(-n) = a^(n-n) = a^0 = 1

So a^(-n) behaves like 1/(a^n) so it is defined to be that.

Other properties involving powers can be 'worked out' using the rules.

eg.  You can work out what a^(0.5) means by considering a^(0.5) x a^(0.5)

Bob

Exponent rules are defined in the textbook and in most basic college algebra courses. Math teachers expect students to memorize the rules rather than to derive them. This is a huge mistake. Bob, isn't this what indoctrination is all about? If not, what is indoctrination?