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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{3}}\right)^{-1}\\= q^{ \frac{2}{3} . (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
2. \(\left(a^{\frac{5}{4}}\right)^{\frac{-3}{5}}\\= a^{ \frac{5}{4} . (\frac{-3}{5}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
3. \(\left(y^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{2} . \frac{1}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
4. \(\left(y^{\frac{5}{4}}\right)^{\frac{1}{4}}\\= y^{ \frac{5}{4} . \frac{1}{4} }= y^{\frac{5}{16}}\\=\sqrt[16]{ y^{5} }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{5}{2}}\\= a^{ 1 . \frac{5}{2} }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
6. \(\left(q^{\frac{-3}{5}}\right)^{\frac{-3}{4}}\\= q^{ \frac{-3}{5} . (\frac{-3}{4}) }= q^{\frac{9}{20}}\\=\sqrt[20]{ q^{9} }\\---------------\)
7. \(\left(x^{\frac{3}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{3}{5} . \frac{1}{2} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
8. \(\left(a^{\frac{1}{6}}\right)^{\frac{-1}{2}}\\= a^{ \frac{1}{6} . (\frac{-1}{2}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{-5}{2}}\\= a^{ -1 . (\frac{-5}{2}) }= a^{\frac{5}{2}}\\= \sqrt{ a^{5} } =|a^{2}|. \sqrt{ a } \\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{1}{2} . \frac{1}{6} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
11. \(\left(y^{\frac{2}{3}}\right)^{\frac{5}{2}}\\= y^{ \frac{2}{3} . \frac{5}{2} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
12. \(\left(a^{\frac{-5}{3}}\right)^{-2}\\= a^{ \frac{-5}{3} . (-2) }= a^{\frac{10}{3}}\\=\sqrt[3]{ a^{10} }=a^{3}.\sqrt[3]{ a }\\---------------\)