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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{3}}\right)^{1}\\= q^{ \frac{2}{3} . 1 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
2. \(\left(q^{\frac{-1}{6}}\right)^{\frac{1}{4}}\\= q^{ \frac{-1}{6} . \frac{1}{4} }= q^{\frac{-1}{24}}\\=\frac{1}{\sqrt[24]{ q }}=\frac{1}{\sqrt[24]{ q }}. \color{purple}{\frac{\sqrt[24]{ q^{23} }}{\sqrt[24]{ q^{23} }}} \\=\frac{\sqrt[24]{ q^{23} }}{|q|}\\---------------\)
3. \(\left(a^{\frac{4}{3}}\right)^{-1}\\= a^{ \frac{4}{3} . (-1) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
4. \(\left(y^{\frac{4}{5}}\right)^{\frac{1}{2}}\\= y^{ \frac{4}{5} . \frac{1}{2} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
5. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-4}{3} . (\frac{-5}{3}) }= q^{\frac{20}{9}}\\=\sqrt[9]{ q^{20} }=q^{2}.\sqrt[9]{ q^{2} }\\---------------\)
6. \(\left(y^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= y^{ \frac{4}{3} . \frac{1}{2} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\left(x^{\frac{1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{1}{2} . (\frac{-1}{2}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
8. \(\left(x^{\frac{4}{5}}\right)^{\frac{-3}{4}}\\= x^{ \frac{4}{5} . (\frac{-3}{4}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
9. \(\left(q^{\frac{-3}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{-3}{2} . \frac{2}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\left(q^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= q^{ \frac{4}{3} . \frac{2}{3} }= q^{\frac{8}{9}}\\=\sqrt[9]{ q^{8} }\\---------------\)
11. \(\left(q^{\frac{-2}{3}}\right)^{-1}\\= q^{ \frac{-2}{3} . (-1) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\left(y^{\frac{5}{3}}\right)^{\frac{-1}{4}}\\= y^{ \frac{5}{3} . (\frac{-1}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)