Algebra 2 high school

Question

Simplify. Assume all variables are positive numbers. Write your answer in only positive exponents.

(27a^-18 b^-12)^2/3

Answer 1

Apply the rules of exponents:  Power to a power.  Also, change the base of 27 so that it is written in exponential form.

 

use the fact that           27 = 3³

 

 

(3³)^2/3 * (a^-18)^2/3 * (b^-12)^2/3

 

 

Now we can multiply the powers for each factor and keep the base.

 

3² * a^-12 * b^-8

 

 

Perform reciprocal to have only positive exponents.

 

9 / (a¹²b⁸)

 

 

 

 

 

Answer 2

(27a^-18b^-12)^2/3

(3³a^-18b^-12)^2/3

3²a^-12b^-8

9 / (a¹²b⁸)