Simplify
√(〖(4)〗^(-2)+(3)^(-2)
To simplify the given expression, we need to simplify the individual terms inside the square root.
Let's start by simplifying the first term: (4)^(-2).
To simplify a negative exponent, we can rewrite it as the reciprocal of the positive exponent. Therefore, (4)^(-2) can be rewritten as 1/(4)^2.
Now, we can simplify the expression further: 1/(4)^2 = 1/16.
Next, let's simplify the second term: (3)^(-2).
Using the same approach, we rewrite (3)^(-2) as 1/(3)^2. Simplifying further, we get 1/9.
Now, we can substitute the simplified values back into the original expression: √((1/16) + (1/9)).
To combine these fractions, we need to find a common denominator. The least common multiple of 16 and 9 is 144.
When we convert the fractions 1/16 and 1/9 to have the common denominator 144, we get 9/144 and 16/144, respectively.
Now, we can combine these fractions: √(9/144 + 16/144) = √(25/144).
To simplify the square root of a fraction, we take the square root of the numerator and the square root of the denominator separately.
√(25/144) = √25 / √144 = 5/12.
Therefore, the simplified form of the given expression √((4)^(-2) + (3)^(-2)) is 5/12.