Expressions with Powers and Roots II

Project ID: 
5000000021
Accepted: 
Template: 
Question: 
The following diagram presents: \( \mathbb{N} \) -- Natural numbers, \( \mathbb{Z} \) -- Integers, \( \mathbb{Q} \) -- Rational numbers, \( \mathbb{R}\setminus \mathbb{Q} \) -- Irrational numbers. In the table, specify the smallest number set to which the given number belongs.
Answer Header 1: 
\( \mathbb{N} \)
Answer Header 2: 
\( \mathbb{Z}\setminus \mathbb{N} \)
Answer Header 3: 
\( \mathbb{Q}\setminus \mathbb{Z} \)
Answer Header 4: 
\( \mathbb{R}\setminus \mathbb{Q} \)
Question Row 1: 
\( 0{,}2^{-1} \)
Answer Row 1: 
1
Question Row 2: 
\( \sqrt{1\frac{1}{16}} \)
Answer Row 2: 
4
Question Row 3: 
\( \left(\frac49\right)^3\cdot\left(\frac8{27}\right)^{-2} \)
Answer Row 3: 
1
Question Row 4: 
\( \left(\sqrt\pi\right)^2 \)
Answer Row 4: 
4
Question Row 5: 
\( (-0{,}5)^{-3} \)
Answer Row 5: 
2
Question Row 6: 
\( \sqrt[3]{-16}\cdot\sqrt[3]{32} \)
Answer Row 6: 
2
Question Row 7: 
\( \sqrt[3]{-15\frac58} \)
Answer Row 7: 
3
Question Row 8: 
\( (128)^{\frac17} \)
Answer Row 8: 
1
Tex: 
% tiket 32669 \pocetsloupcu{4} \let\oldQuestion\Question \def\I{\mathrm{i}} \def\Question{ \begin{minipage}[t]{0.6\linewidth} \leavevmode \kern -20pt \oldQuestion \end{minipage} \hfill \begin{minipage}[t]{0.35\linewidth} \leavevmode \kern -30pt \def\delka{0.3cm} \obrMsr[x=\delka,y=\delka]{0}{10}{0}{10} { \draw[thick] (0,2) -- (10,2) -- (10,10) -- (0,10) -- cycle; \draw[thick] (0,5) -- (10,5); \draw[thick] (1.5,6) -- (1.5,9) -- (8.5,9) -- (8.5,6) -- cycle; \draw[thick] (5,7.5) ellipse (2 and 1); \draw (5,7.5) node[]{$\mathbb{N}$}; \draw (2.25,8) node[]{$\mathbb{Z}$}; \draw (0.75,9) node[]{$\mathbb{Q}$}; \draw (2.25,4) node[]{$\mathbb{R}\setminus\mathbb{Q}$}; } \end{minipage}\vspace*{-3pt}}