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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{2} . \frac{2}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(a^{\frac{-3}{2}}\right)^{\frac{4}{5}}\\= a^{ \frac{-3}{2} . \frac{4}{5} }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
3. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{6} . (\frac{-1}{2}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
4. \(\left(x^{\frac{-1}{6}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{6} . \frac{2}{3} }= x^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ x }}=\frac{1}{\sqrt[9]{ x }}. \color{purple}{\frac{\sqrt[9]{ x^{8} }}{\sqrt[9]{ x^{8} }}} \\=\frac{\sqrt[9]{ x^{8} }}{x}\\---------------\)
5. \(\left(y^{\frac{3}{5}}\right)^{-1}\\= y^{ \frac{3}{5} . (-1) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
6. \(\left(q^{\frac{5}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{5}{3} . (\frac{-1}{5}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
7. \(\left(q^{\frac{-3}{4}}\right)^{\frac{1}{4}}\\= q^{ \frac{-3}{4} . \frac{1}{4} }= q^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ q^{3} }}=\frac{1}{\sqrt[16]{ q^{3} }}. \color{purple}{\frac{\sqrt[16]{ q^{13} }}{\sqrt[16]{ q^{13} }}} \\=\frac{\sqrt[16]{ q^{13} }}{|q|}\\---------------\)
8. \(\left(y^{\frac{2}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{2}{3} . \frac{2}{3} }= y^{\frac{4}{9}}\\=\sqrt[9]{ y^{4} }\\---------------\)
9. \(\left(q^{1}\right)^{1}\\= q^{ 1 . 1 }= q^{1}\\\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{6}}\\= x^{ \frac{-1}{2} . (\frac{-1}{6}) }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
11. \(\left(a^{\frac{4}{3}}\right)^{\frac{-5}{3}}\\= a^{ \frac{4}{3} . (\frac{-5}{3}) }= a^{\frac{-20}{9}}\\=\frac{1}{\sqrt[9]{ a^{20} }}\\=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[9]{ a^{2} }} \color{purple}{\frac{\sqrt[9]{ a^{7} }}{\sqrt[9]{ a^{7} }}} \\=\frac{\sqrt[9]{ a^{7} }}{a^{3}}\\---------------\)
12. \(\left(x^{\frac{4}{5}}\right)^{-1}\\= x^{ \frac{4}{5} . (-1) }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)