# Thread: my last 'simplify the polynomial' problem

1. ## my last 'simplify the polynomial' problem

Last one of this section of my review!

5m^-3
__________
6^-1 m^-2

What steps would I need to take to solve this?

First I would need to do something with the 6^-1. What should I do with it, since the negative power is on the bottom?

After that I'll want to do: -3- (-2), which would be -1, so m^-1, so I would flip that to:

m
___
1

I think.

any input would be greatly appreciated.
THANKS!

2. If the sign of the exponent is negative, it means the number/variable/expression is in the "wrong" side of the fraction.

2 is a fraction. It is 2/1.
So, a^(-2) is a fraction too. It is a^(-2) / 1.
The -2 exponent of "a" means a is in the "wrong" side of the fraction. To eliminate the negative sign, just place the "a" in its correct side. If the numerator side is the "wrong" side, then the denominator side must be the "correct" side.
so, a^(-2) = 1 / (a^2)

and, 3 / [5^(-m)] = 3*5^m

and, m^(-3) / [-(3^(-m))]
= 3^m / [-1 *m^3]
= 3^m / [-(m^3)]

Okay. So,

5m^-3
__________
6^-1 m^-2

= 5*(6^1)(m^2) / m^3

-----------------------------------------
Or, if you don't want to be bothered by putting the expressions in their "correct" sides in the fraction, then just use the exponent rules.
a^b * a^c = a^(b+c)
a^b / a^c = a^(b -c)

5m^-3
__________
6^-1 m^-2

= 5*(6^1)[m^(-3 -(-2))]
= 5(6)[m^(-1)]
= 30m^(-1) --------------------same as above.

3. Originally Posted by ticbol
If the sign of the exponent is negative, it means the number/variable/expression is in the "wrong" side of the fraction.

2 is a fraction. It is 2/1.
So, a^(-2) is a fraction too. It is a^(-2) / 1.
The -2 exponent of "a" means a is in the "wrong" side of the fraction. To eliminate the negative sign, just place the "a" in its correct side. If the numerator side is the "wrong" side, then the denominator side must be the "correct" side.
so, a^(-2) = 1 / (a^2)

and, 3 / [5^(-m)] = 3*5^m

and, m^(-3) / [-(3^(-m))]
= 3^m / [-1 *m^3]
= 3^m / [-(m^3)]

Okay. So,

5m^-3
__________
6^-1 m^-2

= 5*(6^1)(m^2) / m^3

-----------------------------------------
Or, if you don't want to be bothered by putting the expressions in their "correct" sides in the fraction, then just use the exponent rules.
a^b * a^c = a^(b+c)
a^b / a^c = a^(b -c)

5m^-3
__________
6^-1 m^-2

= 5*(6^1)[m^(-3 -(-2))]
= 5(6)[m^(-1)]
= 30m^(-1) --------------------same as above.

thanks! that totally makes sense