SOLUTION: If z = 2¹⁴∙3²⁰, what is the largest power of 12 that evenly divides into the square root of z?

If z = 214∙320, what is the largest 
power of 12 that evenly divides into the square root of z?



Let p = the largest power of 12 that evenly divides into the
square root of z





We are given:



We find the square root of z





Now we divide  INTO , which amounts to
dividing  BY 



Subtracting exponents on the right



Negative exponents cause denominators. Therefore both those 
exponents must be non-negative (greater than or equal to zero) 
in order for the above result to be an integer, so we have:

 and 

 and 

Remember that the inequality reverses when dividing 
by a negative number:

 and 

  and 

 and 

The largest integer value of p that satisfies both those is p = 3.

Answer: The largest power of 12 that evenly divides into the square 
root of z is 3.

Edwin