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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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