Answer:
1/3
Step-by-step explanation:
To simplify the expression (3^-1 * 9^-1) / 3^-2, let's break it down step by step:
Step 1: Simplify the exponents
First, let's simplify the exponents in the expression.
3^-1 is the same as 1/3^1, which equals 1/3.
Similarly, 9^-1 is the same as 1/9^1, which equals 1/9.
3^-2 is the same as 1/3^2, which equals 1/9.
So, the expression becomes (1/3 * 1/9) / (1/9).
Step 2: Simplify the multiplication and division
Next, let's simplify the multiplication and division in the expression.
When we multiply fractions, we multiply the numerators and multiply the denominators. So, (1/3 * 1/9) equals 1/27.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, (1/27) / (1/9) equals (1/27) * (9/1), which is 9/27.
Step 3: Simplify the fraction
Finally, let's simplify the fraction 9/27.
Both 9 and 27 are divisible by 9. Dividing both numerator and denominator by 9, we get 1/3.
Therefore, the expression (3^-1 * 9^-1) / 3^-2 simplifies to 1/3.
If you have any further questions, feel free to ask.
