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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{6} . \frac{1}{2} }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
2. \(\left(x^{\frac{-2}{3}}\right)^{\frac{5}{2}}\\= x^{ \frac{-2}{3} . \frac{5}{2} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
3. \(\left(a^{\frac{-3}{4}}\right)^{1}\\= a^{ \frac{-3}{4} . 1 }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
4. \(\left(x^{1}\right)^{\frac{-3}{4}}\\= x^{ 1 . (\frac{-3}{4}) }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
5. \(\left(a^{\frac{2}{3}}\right)^{\frac{-1}{5}}\\= a^{ \frac{2}{3} . (\frac{-1}{5}) }= a^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ a^{2} }}=\frac{1}{\sqrt[15]{ a^{2} }}. \color{purple}{\frac{\sqrt[15]{ a^{13} }}{\sqrt[15]{ a^{13} }}} \\=\frac{\sqrt[15]{ a^{13} }}{a}\\---------------\)
6. \(\left(x^{\frac{4}{3}}\right)^{\frac{3}{4}}\\= x^{ \frac{4}{3} . \frac{3}{4} }= x^{1}\\\\---------------\)
7. \(\left(y^{-1}\right)^{\frac{2}{5}}\\= y^{ -1 . \frac{2}{5} }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
8. \(\left(x^{\frac{5}{3}}\right)^{1}\\= x^{ \frac{5}{3} . 1 }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
9. \(\left(a^{\frac{1}{6}}\right)^{\frac{5}{6}}\\= a^{ \frac{1}{6} . \frac{5}{6} }= a^{\frac{5}{36}}\\=\sqrt[36]{ a^{5} }\\---------------\)
10. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-1}{4}}\\= a^{ \frac{-5}{6} . (\frac{-1}{4}) }= a^{\frac{5}{24}}\\=\sqrt[24]{ a^{5} }\\---------------\)
11. \(\left(y^{\frac{3}{5}}\right)^{\frac{2}{3}}\\= y^{ \frac{3}{5} . \frac{2}{3} }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
12. \(\left(q^{\frac{-2}{3}}\right)^{1}\\= q^{ \frac{-2}{3} . 1 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)