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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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