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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{1}{3} . \frac{1}{4} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
2. \(\left(x^{\frac{-3}{4}}\right)^{\frac{4}{3}}\\= x^{ \frac{-3}{4} . \frac{4}{3} }= x^{-1}\\=\frac{1}{x}\\---------------\)
3. \(\left(q^{\frac{1}{3}}\right)^{1}\\= q^{ \frac{1}{3} . 1 }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
4. \(\left(x^{-1}\right)^{\frac{1}{3}}\\= x^{ -1 . \frac{1}{3} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
5. \(\left(q^{\frac{-2}{3}}\right)^{\frac{-5}{3}}\\= q^{ \frac{-2}{3} . (\frac{-5}{3}) }= q^{\frac{10}{9}}\\=\sqrt[9]{ q^{10} }=q.\sqrt[9]{ q }\\---------------\)
6. \(\left(y^{\frac{3}{5}}\right)^{\frac{5}{4}}\\= y^{ \frac{3}{5} . \frac{5}{4} }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
7. \(\left(x^{\frac{4}{5}}\right)^{\frac{1}{5}}\\= x^{ \frac{4}{5} . \frac{1}{5} }= x^{\frac{4}{25}}\\=\sqrt[25]{ x^{4} }\\---------------\)
8. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{-1}{3} . \frac{1}{3} }= a^{\frac{-1}{9}}\\=\frac{1}{\sqrt[9]{ a }}=\frac{1}{\sqrt[9]{ a }}. \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a}\\---------------\)
9. \(\left(x^{\frac{-3}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{-3}{5} . \frac{5}{4} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
10. \(\left(x^{\frac{-2}{3}}\right)^{\frac{3}{5}}\\= x^{ \frac{-2}{3} . \frac{3}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
11. \(\left(q^{\frac{1}{3}}\right)^{2}\\= q^{ \frac{1}{3} . 2 }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{6}}\\= a^{ \frac{4}{5} . \frac{1}{6} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)