(2/3)^-2 + (-4)^-2
To simplify the expression (2/3)^-2 + (-4)^-2, we need to understand the concept of negative exponents.
In mathematics, a negative exponent indicates the reciprocal of the corresponding positive exponent. For example, a^(-n) is equal to 1/a^n.
Using this rule, let's simplify each term individually:
1. (2/3)^-2:
Here, the negative exponent applies to the entire fraction (2/3), so we need to find its reciprocal. The reciprocal of 2/3 is 3/2.
Therefore, (2/3)^-2 = (3/2)^2 = 9/4.
2. (-4)^-2:
Similarly, the negative exponent applies to the entire number (-4), so we need to find its reciprocal. The reciprocal of -4 is -1/4.
Therefore, (-4)^-2 = (-1/4)^2 = 1/16.
Now, we can find the sum of the two simplified terms:
9/4 + 1/16.
To add these fractions, we need a common denominator, which in this case is 16. So, we rewrite 9/4 as an equivalent fraction with a denominator of 16:
9/4 = (9/4) * (4/4) = 36/16.
Now we can add the fractions:
36/16 + 1/16 = 37/16.
So, the simplified sum of (2/3)^-2 + (-4)^-2 is 37/16.