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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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