(3^3 times 2^-4)^4/3^6

To simplify the expression, let's break it down step by step:

First, let's simplify the exponent of 3^3 and 2^-4:
3^3 = 3 * 3 * 3 = 27 (since 3 raised to the power of 3 is 27)
2^-4 = 1 / 2^4 = 1 / (2 * 2 * 2 * 2) = 1 / 16

Now, let's substitute the simplified values back into the expression:
(27 * (1 / 16))^4 / 3^6

Next, let's simplify the numerator:
27 * (1 / 16) = 27 / 16

Substituting the simplified numerator and denominator into the expression:
(27 / 16)^4 / 3^6

To simplify the expression further, let's evaluate the numerator and denominator separately:

Numerator: (27 / 16)^4
To raise a fraction to a power, you raise both the numerator and denominator to that power:
27^4 / 16^4 = 531441 / 65536

Denominator: 3^6 = 3 * 3 * 3 * 3 * 3 * 3 = 729

Now, we can substitute the simplified numerator and denominator back into the expression:
(531441 / 65536) / 729

To divide by a fraction, we multiply by its reciprocal:
(531441 / 65536) * (1 / 729)

Next, let's simplify the fraction:
531441 * 1 / 65536 * 729 = 531441 / (65536 * 729)

Now, let's multiply the values in the denominator:
65536 * 729 = 47829696

Substituting the simplified numerator and denominator back into the expression:
531441 / 47829696

This is the simplified form of the expression (3^3 times 2^-4)^4/3^6.