If in index notation there are variables and numbers and question says to simplify and give answer as positive index then
Is 1/3^2a^2 is it correct after simplifying all negative indices
Or should we make it as 1/9a^2
Can we leave as 3^2? Or both Answers acceptable?
I know that if question says simplify and Evaluate then numbers need to be multiplied depending on exponent
What "negative indices"?
What happened to "a" in your second alternative?
I would go with 1/9a^2.
Second alternative I mean
1/3^2 a^2 ( leaving answer with positive index form as question said simplify and leave as positive index) Won’t this be fine too?
Unless question said Simplify then I wouldn’t leave any exponent form. Since the question said simplify and give answer as positive index
To simplify the expression 1/3^(2a^2) and write it in positive index form, we can follow these steps:
Step 1: Simplify the negative index.
To simplify a negative index, we can rewrite it as the reciprocal of the base raised to the positive index. In this case, 3^(-2a^2) can be written as (1/3^(2a^2)).
Step 2: Simplify the expression further.
Now, we have 1/3^(2a^2). Since the base (3) is the same for both the numerator and denominator, we can subtract the exponents in the denominator from the exponent in the numerator.
So, we subtract 2a^2 from 0 (the implied exponent in the numerator for 1) and get -2a^2 as the exponent in the denominator.
Therefore, the simplified expression becomes 1/3^(-2a^2), which can be rewritten as (3^(2a^2)).
To write the expression in positive index form, we simply take the reciprocal of the expression.
So, the final answer in positive index form is 1/(3^(2a^2)), or we can also write it as 1/9a^2.
Both answers, (3^(2a^2)) and 1/9a^2, are acceptable and equivalent.