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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{3}}\right)^{\frac{-5}{2}}\\= y^{ \frac{1}{3} . (\frac{-5}{2}) }= y^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ y^{5} }}=\frac{1}{\sqrt[6]{ y^{5} }}. \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y|}\\---------------\)
2. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-4}{3}}\\= q^{ \frac{-5}{4} . (\frac{-4}{3}) }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
3. \(\left(y^{\frac{-5}{2}}\right)^{\frac{5}{2}}\\= y^{ \frac{-5}{2} . \frac{5}{2} }= y^{\frac{-25}{4}}\\=\frac{1}{\sqrt[4]{ y^{25} }}\\=\frac{1}{|y^{6}|.\sqrt[4]{ y }}=\frac{1}{|y^{6}|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{7}|}\\---------------\)
4. \(\left(q^{-1}\right)^{\frac{5}{4}}\\= q^{ -1 . \frac{5}{4} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
5. \(\left(a^{\frac{-5}{4}}\right)^{\frac{5}{2}}\\= a^{ \frac{-5}{4} . \frac{5}{2} }= a^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ a^{25} }}\\=\frac{1}{|a^{3}|.\sqrt[8]{ a }}=\frac{1}{|a^{3}|.\sqrt[8]{ a }} \color{purple}{\frac{\sqrt[8]{ a^{7} }}{\sqrt[8]{ a^{7} }}} \\=\frac{\sqrt[8]{ a^{7} }}{|a^{4}|}\\---------------\)
6. \(\left(x^{\frac{1}{5}}\right)^{\frac{-1}{3}}\\= x^{ \frac{1}{5} . (\frac{-1}{3}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
7. \(\left(x^{\frac{2}{5}}\right)^{-1}\\= x^{ \frac{2}{5} . (-1) }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
8. \(\left(q^{\frac{-4}{3}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-4}{3} . (\frac{-5}{2}) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{5}}\\= q^{ \frac{1}{2} . (\frac{-3}{5}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
10. \(\left(q^{1}\right)^{\frac{5}{4}}\\= q^{ 1 . \frac{5}{4} }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
11. \(\left(y^{\frac{5}{6}}\right)^{\frac{-2}{5}}\\= y^{ \frac{5}{6} . (\frac{-2}{5}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
12. \(\left(y^{1}\right)^{\frac{1}{6}}\\= y^{ 1 . \frac{1}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)