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Werk uit m.b.v. de rekenregels

1. \(\left(y^{1}\right)^{1}\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{3}}\)
3. \(\left(y^{-1}\right)^{\frac{1}{2}}\)
4. \(\left(a^{\frac{-1}{2}}\right)^{-1}\)
5. \(\left(a^{\frac{-3}{2}}\right)^{\frac{3}{5}}\)
6. \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{2}}\)
7. \(\left(y^{1}\right)^{-2}\)
8. \(\left(y^{\frac{-5}{2}}\right)^{\frac{5}{4}}\)
9. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{2}}\)
10. \(\left(a^{\frac{5}{3}}\right)^{\frac{-2}{5}}\)
11. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{3}}\)
12. \(\left(q^{\frac{4}{5}}\right)^{\frac{-5}{3}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{1}{3}}\\= x^{ \frac{-1}{2} . \frac{1}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
3. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\left(a^{\frac{-1}{2}}\right)^{-1}\\= a^{ \frac{-1}{2} . (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
5. \(\left(a^{\frac{-3}{2}}\right)^{\frac{3}{5}}\\= a^{ \frac{-3}{2} . \frac{3}{5} }= a^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ a^{9} }}=\frac{1}{\sqrt[10]{ a^{9} }}. \color{purple}{\frac{\sqrt[10]{ a }}{\sqrt[10]{ a }}} \\=\frac{\sqrt[10]{ a }}{|a|}\\---------------\)
6. \(\left(x^{\frac{2}{3}}\right)^{\frac{1}{2}}\\= x^{ \frac{2}{3} . \frac{1}{2} }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
7. \(\left(y^{1}\right)^{-2}\\= y^{ 1 . (-2) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
8. \(\left(y^{\frac{-5}{2}}\right)^{\frac{5}{4}}\\= y^{ \frac{-5}{2} . \frac{5}{4} }= y^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ y^{25} }}\\=\frac{1}{|y^{3}|.\sqrt[8]{ y }}=\frac{1}{|y^{3}|.\sqrt[8]{ y }} \color{purple}{\frac{\sqrt[8]{ y^{7} }}{\sqrt[8]{ y^{7} }}} \\=\frac{\sqrt[8]{ y^{7} }}{|y^{4}|}\\---------------\)
9. \(\left(q^{\frac{1}{5}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{5} . (\frac{-1}{2}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
10. \(\left(a^{\frac{5}{3}}\right)^{\frac{-2}{5}}\\= a^{ \frac{5}{3} . (\frac{-2}{5}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{1}{2} . (\frac{-4}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
12. \(\left(q^{\frac{4}{5}}\right)^{\frac{-5}{3}}\\= q^{ \frac{4}{5} . (\frac{-5}{3}) }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)