The given expression is:Given the equation:
[tex](-\frac{1}{3})^2+\sqrt[3]{3^4+44}[/tex]The first step is to solve the expression in parentheses, so:
[tex]\begin{gathered} (-\frac{1}{3})^2=(-\frac{1}{3})\times(-\frac{1}{3}) \\ \\ \text{ By applying the properties of fractions:} \\ =\frac{(-1)\times(-1)}{3\times3}=\frac{1}{9} \end{gathered}[/tex]Now, we have:
[tex]\frac{1}{9}+\sqrt[3]{3^4+44}[/tex]Solve the expression in the root:
[tex]\begin{gathered} 3^4=3\times3\times3\times3=81 \\ 81+44=125 \end{gathered}[/tex]We can rewrite the expression as:
[tex]\frac{1}{9}+\sqrt[3]{125}\text{ This is the first answer option that is correct}[/tex]Let's continue:
[tex]\begin{gathered} \sqrt[3]{125}=5 \\ \text{ So:} \\ \frac{1}{9}+5 \end{gathered}[/tex]This is the second answer answer option that is correct.
And finally:
[tex]\frac{1}{9}+5=\frac{(1\times1)+(9\times5)}{9\times1}=\frac{1+45}{9}=\frac{46}{9}[/tex]46/9 is the last option that is correct.
[tex](x-21)^2\text{ = 25}[/tex]Let's simplify the equation to be able to get the solution. We get,
[tex](x-21)^2\text{ = 25}[/tex]