Apply the laws of exponents to simplify the following: 3^3n / (27)^2nShow complete solution to explain the answer.

the laws of exponentials state that when SAME-based
exponentials divide, the exponentials subtract each other. In math
notation

X^A-X^B=X^(A-B)

well,
in this case, we still do not see a common base. However, we know that 27 =
3^3

so the denominator (27)^2n=
(3^3)^2n

by law of exponentials, a exponent's exponent
result in the exponents timed
together

(3^3)^2n=3^6n

the
original equation becomes:

3^3n/3^6n which using the
exponential law of division

= 3^(3n-6n)= 3 ^
(-3n)

well if your teacher allows you to write in negative
exponents, ust keep the answer, if not, continue
simplify:

by the law of mutiplying exponents
again

3^(-3n)=
(3^3)^-n=27^(-n)

by the law of negative
exponents

27^(-n)=1/(27^n)

Well,
you could also change the numerator 3^3n into 27^n first so that the base is both 27, do
whatever you think is easier.

Hope this
helps