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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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