Answer: 3^16.
Explanation:
To find the greatest common monomial factor of three times twenty-seven raised to the fifth power, you can break down the numbers and simplify:
3 * 27^5
First, simplify 27^5:
27^5 = (3^3)^5 = 3^(3*5) = 3^15
Now, substitute this back into the original expression:
3 * 3^15
To find the greatest common monomial factor, you need to factor out the common base, which is 3:
3 * 3^15 = 3^(1+15) = 3^16
So, the greatest common monomial factor of three times twenty-seven raised to the fifth power is 3^16.