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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{4}}\right)^{1}\\= x^{ \frac{-3}{4} . 1 }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
2. \(\left(q^{\frac{1}{4}}\right)^{\frac{5}{2}}\\= q^{ \frac{1}{4} . \frac{5}{2} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
3. \(\left(y^{\frac{-5}{4}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-5}{4} . (\frac{-5}{4}) }= y^{\frac{25}{16}}\\=\sqrt[16]{ y^{25} }=|y|.\sqrt[16]{ y^{9} }\\---------------\)
4. \(\left(q^{\frac{-1}{3}}\right)^{\frac{4}{5}}\\= q^{ \frac{-1}{3} . \frac{4}{5} }= q^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ q^{4} }}=\frac{1}{\sqrt[15]{ q^{4} }}. \color{purple}{\frac{\sqrt[15]{ q^{11} }}{\sqrt[15]{ q^{11} }}} \\=\frac{\sqrt[15]{ q^{11} }}{q}\\---------------\)
5. \(\left(a^{\frac{3}{5}}\right)^{-1}\\= a^{ \frac{3}{5} . (-1) }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)
6. \(\left(y^{\frac{4}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{4}{3} . \frac{2}{3} }= y^{\frac{8}{9}}\\=\sqrt[9]{ y^{8} }\\---------------\)
7. \(\left(x^{1}\right)^{\frac{5}{6}}\\= x^{ 1 . \frac{5}{6} }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
8. \(\left(y^{\frac{-3}{4}}\right)^{-1}\\= y^{ \frac{-3}{4} . (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
9. \(\left(x^{1}\right)^{\frac{-1}{4}}\\= x^{ 1 . (\frac{-1}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{\frac{1}{5}}\\= a^{ \frac{2}{3} . \frac{1}{5} }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
11. \(\left(y^{\frac{2}{5}}\right)^{1}\\= y^{ \frac{2}{5} . 1 }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
12. \(\left(x^{\frac{1}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{1}{3} . (\frac{-2}{3}) }= x^{\frac{-2}{9}}\\=\frac{1}{\sqrt[9]{ x^{2} }}=\frac{1}{\sqrt[9]{ x^{2} }}. \color{purple}{\frac{\sqrt[9]{ x^{7} }}{\sqrt[9]{ x^{7} }}} \\=\frac{\sqrt[9]{ x^{7} }}{x}\\---------------\)