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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{2}{3}}\right)^{\frac{4}{3}}\\= x^{ \frac{2}{3} . \frac{4}{3} }= x^{\frac{8}{9}}\\=\sqrt[9]{ x^{8} }\\---------------\)
2. \(\left(x^{\frac{3}{2}}\right)^{\frac{4}{3}}\\= x^{ \frac{3}{2} . \frac{4}{3} }= x^{2}\\\\---------------\)
3. \(\left(y^{\frac{1}{5}}\right)^{\frac{-4}{3}}\\= y^{ \frac{1}{5} . (\frac{-4}{3}) }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
4. \(\left(q^{\frac{-1}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{-1}{4} . (\frac{-5}{6}) }= q^{\frac{5}{24}}\\=\sqrt[24]{ q^{5} }\\---------------\)
5. \(\left(y^{\frac{-2}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{-2}{3} . \frac{2}{3} }= y^{\frac{-4}{9}}\\=\frac{1}{\sqrt[9]{ y^{4} }}=\frac{1}{\sqrt[9]{ y^{4} }}. \color{purple}{\frac{\sqrt[9]{ y^{5} }}{\sqrt[9]{ y^{5} }}} \\=\frac{\sqrt[9]{ y^{5} }}{y}\\---------------\)
6. \(\left(q^{\frac{-4}{5}}\right)^{\frac{5}{4}}\\= q^{ \frac{-4}{5} . \frac{5}{4} }= q^{-1}\\=\frac{1}{q}\\---------------\)
7. \(\left(a^{\frac{4}{3}}\right)^{\frac{-3}{5}}\\= a^{ \frac{4}{3} . (\frac{-3}{5}) }= a^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ a^{4} }}=\frac{1}{\sqrt[5]{ a^{4} }}. \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a}\\---------------\)
8. \(\left(a^{-1}\right)^{\frac{-4}{5}}\\= a^{ -1 . (\frac{-4}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
9. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{5}{3} . (\frac{-1}{2}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
10. \(\left(x^{\frac{1}{2}}\right)^{-1}\\= x^{ \frac{1}{2} . (-1) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
11. \(\left(x^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= x^{ \frac{-5}{2} . \frac{1}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
12. \(\left(q^{\frac{3}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{3}{2} . (\frac{-2}{3}) }= q^{-1}\\=\frac{1}{q}\\---------------\)