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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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