simplifing (3a^3)^(-3) ÷ (6a^(-3))^2

[zhyia]

simplifing (3a^3)^(-3) ÷ (6a^(-3))^2

(3a³)ˉ³ ÷ (6aˉ³)²

 

[stapel]

A good first step would be to write the expressions without negative exponents, and then convert the "divided by (the resulting fraction)" into "multiplied by (the reciprocal)".

If you get stuck in the process, please reply showing how far you have gotten. Thank you.

Eliz.

 

[zhyia]

i did it like this 27a^9/ 1/36a^6 but im not sure it was done correctly

 

[stapel]

i did it like this 27a^9/ 1/36a^6....

How did you arrive at this stage?

For instance, how did you get that (3a³)^-3 = 27a⁹ = (3a³)³, rather than (3a³)^-3 = 1/(3a³)³ = 1/(27a⁹)?

Please reply showing all of your steps. Thank you.

Eliz.

 

[pka]

The student needs to study this:
\(\displaystyle \L
\frac{{\left( {3a^3 } \right)^{ - 3} }}{{\left( {6a^{ - 3} } \right)^2 }} = \frac{{3^{ - 3} a^{ - 9} }}{{6^2 a^{ - 6} }} = \frac{1}{{\left( {36} \right)\left( {27} \right)a^3 }}\)

 

[zhyia]

is this the final answer...thats how i should have worked out the problem?

 

[Denis]

is this the final answer...thats how i should have worked out the problem?

YESSSSSSSS...but do you understand what pka did?

 

[zhyia]

yes...i do now