# Struggling a bit on (6m^4)^-2 x 9m^-3

#### SaltyPoro

##### New member
I'm having trouble simplifying this question below
(6m4)-2 x 9m-3
I've done up to 6m-8 x 9m-3 but I have no idea how to get to the answer which is 9/m11

#### mmm4444bot

##### Super Moderator
Staff member
(6m4)-2 x 9m-3
I've done up to 6m-8 x 9m-3
The exponent (-2) applies to both factors inside the grouping symbols (i.e., the 6 and the m4).

Remember the property:

(a·b)^n = a^n · b^n

… I have no idea how to get to the answer which is 9/m11
That's not the correct answer. Are you sure you typed the given expression correctly?

#### SaltyPoro

##### New member
The exponent -2 applies to both the 6 and the m4.

Remember the property:

(a·b)^n = a^n · b^n

That's not the correct answer. Are you sure you typed the given expression correctly?
The answer sheet on the bottom of the page had the answer as 9/m11 (As a fraction).
I'm pretty sure I typed the expression correctly, the following is as it appears of the worksheet (6m^4)^-2 · 9m^-3
The notes I have are (am)n = amn. I assumed the 6 would stay the same because all the questions that had been done in my book were done the same way.
E.g. Simplify (10^6)^2 = 10^12

#### mmm4444bot

##### Super Moderator
Staff member
The answer sheet on the bottom of the page had the answer as 9/m11 (As a fraction).
I'm pretty sure I typed the expression correctly, the following is as it appears of the worksheet (6m^4)^-2 · 9m^-3
There's a mistake somewhere in your materials. If we delete the 6, the answer becomes 9/m^11.

The notes I have are (am)n = amn. I assumed the 6 would stay the same because all the questions that had been done in my book were done the same way.
E.g. Simplify (10^6)^2 = 10^12
Your example is a different form. When you have a product being raised to a power, each factor in the product gets raised to the power.

(a·b)^n = a^n · b^n

EG: (6·10^6)^2 = 6^2 · 10^12

Maybe this property will be on your next worksheet! :cool:

#### mmm4444bot

##### Super Moderator
Staff member
You ought to have the definition of negative exponents, in your notes, too.

m^(-8) = 1/m^8

Yes?

#### SaltyPoro

##### New member
You ought to have the definition of negative exponents, in your notes, too.

m^(-8) = 1/m^8

Yes?
Yep, I have that in my notes.

#### mmm4444bot

##### Super Moderator
Staff member
If you delete the 6 from the original exercise, can you get the given answer? :cool:

#### SaltyPoro

##### New member
If you delete the 6 from the original exercise, can you get the given answer? :cool:
Yes. ;-;
I spent ages trying to figure this question out, didn't realise there was a mistake in the sheet .

#### mmm4444bot

##### Super Moderator
Staff member
If one of your earlier attempts on the exericse as given yielded 1/(4m^11), then you did good.