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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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