Final answer:
The expression 1/9 times 27 simplifies to 1, as 27 is equivalent to 3³ and when you divide it by 1/9 (which can be thought of as 3¹), you get 3², and 3² cancels out the 1/9, resulting in 1.
Step-by-step explanation:
The expression in question is 1/9 times 27. Remember, when dealing with exponents, the exponent applies to everything inside the parentheses. Here, however, the expression is simple and does not involve any parentheses. We are just multiplying the fraction 1/9 by the number 27. To simplify this expression, we can look at it as 27 being 3 to the power of 3 (since 27 is equivalent to 3³). So the expression can also be written as (1/9) × (3³). We have 3¹ in the denominator and 3³ in the numerator. According to the properties of exponents, when dividing like bases, one can subtract the exponents, so 3³ divided by 3¹ is the same as 3 to the power of (3 - 1), which is 3² or 9. Therefore, the expression simplifies to (1/9) × 9. Multiplying 1/9 by 9 simply gives us 1. So, the expression 1/9 times 27 is equivalent to 1.