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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{-1}\\= q^{ -1 . (-1) }= q^{1}\\\\---------------\)
2. \(\left(a^{1}\right)^{\frac{2}{3}}\\= a^{ 1 . \frac{2}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(y^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= y^{ \frac{-5}{6} . \frac{1}{2} }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
4. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-3}{5}}\\= x^{ \frac{-1}{4} . (\frac{-3}{5}) }= x^{\frac{3}{20}}\\=\sqrt[20]{ x^{3} }\\---------------\)
5. \(\left(a^{\frac{5}{4}}\right)^{\frac{3}{2}}\\= a^{ \frac{5}{4} . \frac{3}{2} }= a^{\frac{15}{8}}\\=\sqrt[8]{ a^{15} }=|a|.\sqrt[8]{ a^{7} }\\---------------\)
6. \(\left(a^{\frac{1}{6}}\right)^{\frac{-3}{2}}\\= a^{ \frac{1}{6} . (\frac{-3}{2}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
7. \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{5}}\\= y^{ \frac{-1}{2} . \frac{2}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
8. \(\left(x^{\frac{-2}{5}}\right)^{\frac{1}{4}}\\= x^{ \frac{-2}{5} . \frac{1}{4} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
9. \(\left(y^{\frac{-5}{6}}\right)^{\frac{-1}{3}}\\= y^{ \frac{-5}{6} . (\frac{-1}{3}) }= y^{\frac{5}{18}}\\=\sqrt[18]{ y^{5} }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{3}{4}}\\= q^{ \frac{1}{2} . \frac{3}{4} }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
11. \(\left(q^{\frac{5}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{5}{2} . (\frac{-3}{4}) }= q^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ q^{15} }}\\=\frac{1}{|q|.\sqrt[8]{ q^{7} }}=\frac{1}{|q|.\sqrt[8]{ q^{7} }} \color{purple}{\frac{\sqrt[8]{ q }}{\sqrt[8]{ q }}} \\=\frac{\sqrt[8]{ q }}{|q^{2}|}\\---------------\)
12. \(\left(a^{-1}\right)^{\frac{4}{5}}\\= a^{ -1 . \frac{4}{5} }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)