what is (3^3 times 2^-4)^4/3^6.
To solve this expression, we'll perform the calculations step by step:
First, we simplify the expression inside the parentheses:
3^3 = 3 * 3 * 3 = 27
2^-4 = 1/(2^4) = 1/16
So, (3^3 * 2^-4) = 27 * 1/16 = 27/16
Now, let's simplify the overall expression:
(27/16)^4 / 3^6
To simplify the numerator:
(27/16)^4 = (27^4)/(16^4) = 531,441/65,536
To simplify the denominator:
3^6 = 3 * 3 * 3 * 3 * 3 * 3 = 729
Now, we can rewrite the expression as:
(531,441/65,536) / 729
To divide fractions, we multiply the numerator by the reciprocal of the denominator:
(531,441/65,536) * (1/729)
Let's simplify this expression further:
(531,441 * 1)/(65,536 * 729)
531,441/47,834,624
The final simplified expression is 531,441/47,834,624.