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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{3}}\right)^{2}\\= q^{ \frac{1}{3} . 2 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(a^{\frac{1}{5}}\right)^{\frac{1}{2}}\\= a^{ \frac{1}{5} . \frac{1}{2} }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
3. \(\left(y^{\frac{5}{6}}\right)^{\frac{-3}{5}}\\= y^{ \frac{5}{6} . (\frac{-3}{5}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
4. \(\left(y^{\frac{-5}{2}}\right)^{1}\\= y^{ \frac{-5}{2} . 1 }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
5. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
6. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-5}{4} . (\frac{-3}{4}) }= q^{\frac{15}{16}}\\=\sqrt[16]{ q^{15} }\\---------------\)
7. \(\left(q^{\frac{-2}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-2}{5} . (\frac{-3}{4}) }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
8. \(\left(q^{-1}\right)^{\frac{-2}{3}}\\= q^{ -1 . (\frac{-2}{3}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
9. \(\left(a^{\frac{-1}{2}}\right)^{\frac{3}{4}}\\= a^{ \frac{-1}{2} . \frac{3}{4} }= a^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ a^{3} }}=\frac{1}{\sqrt[8]{ a^{3} }}. \color{purple}{\frac{\sqrt[8]{ a^{5} }}{\sqrt[8]{ a^{5} }}} \\=\frac{\sqrt[8]{ a^{5} }}{|a|}\\---------------\)
10. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-4}{5} . (\frac{-1}{2}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
11. \(\left(a^{-1}\right)^{\frac{-1}{3}}\\= a^{ -1 . (\frac{-1}{3}) }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
12. \(\left(x^{-2}\right)^{-1}\\= x^{ -2 . (-1) }= x^{2}\\\\---------------\)