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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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