Let's look carefully at statement (a):
To determine if [tex]\(\left(\frac{3}{11}\right)^{-2}\)[/tex] is a whole number, we need to follow these steps:
1. First, consider the expression [tex]\(\left(\frac{3}{11}\right)^{-2}\)[/tex]. The negative exponent means we take the reciprocal of the base and then raise it to the positive exponent. So, [tex]\(\left(\frac{3}{11}\right)^{-2} = \left(\frac{11}{3}\right)^{2}\)[/tex].
2. Next, compute [tex]\(\left(\frac{11}{3}\right)^{2}\)[/tex]:
[tex]\[
\left(\frac{11}{3}\right)^{2} = \frac{11^2}{3^2} = \frac{121}{9}
\][/tex]
3. Now, [tex]\(\frac{121}{9}\)[/tex] is a fraction, not a whole number. A whole number is an integer without a fractional or decimal part.
Therefore, [tex]\(\left(\frac{3}{11}\right)^{-2}\)[/tex] is not a whole number.
Given this analysis, the statement (a) is:
False
Since only part (a) is provided in the question, no further steps for part (b) are available.
