To simplify [tex]\(-\frac{1}{16} \div \left(4 - \frac{17}{4}\right)^2\)[/tex], let's go through it step-by-step.
1. Simplify the term inside the parentheses:
[tex]\[
4 - \frac{17}{4}
\][/tex]
2. Convert 4 to a fraction with a common denominator:
[tex]\[
4 = \frac{16}{4}
\][/tex]
3. Subtract the fractions:
[tex]\[
\frac{16}{4} - \frac{17}{4} = \frac{16 - 17}{4} = \frac{-1}{4}
\][/tex]
4. Square the result:
[tex]\[
\left(\frac{-1}{4}\right)^2 = \frac{1}{16}
\][/tex]
5. Divide [tex]\(-\frac{1}{16}\)[/tex] by the squared result:
[tex]\[
-\frac{1}{16} \div \frac{1}{16}
\][/tex]
6. Recognize that dividing by a fraction is equivalent to multiplying by its reciprocal:
[tex]\[
-\frac{1}{16} \times \frac{16}{1} = -1
\][/tex]
So, the simplified result is:
[tex]\[
-1
\][/tex]
