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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-5}{4} . (\frac{-2}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
2. \(\left(a^{2}\right)^{\frac{5}{6}}\\= a^{ 2 . \frac{5}{6} }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
3. \(\left(y^{\frac{3}{5}}\right)^{\frac{-3}{4}}\\= y^{ \frac{3}{5} . (\frac{-3}{4}) }= y^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ y^{9} }}=\frac{1}{\sqrt[20]{ y^{9} }}. \color{purple}{\frac{\sqrt[20]{ y^{11} }}{\sqrt[20]{ y^{11} }}} \\=\frac{\sqrt[20]{ y^{11} }}{|y|}\\---------------\)
4. \(\left(q^{\frac{-5}{2}}\right)^{2}\\= q^{ \frac{-5}{2} . 2 }= q^{-5}\\=\frac{1}{q^{5}}\\---------------\)
5. \(\left(q^{\frac{1}{3}}\right)^{\frac{1}{4}}\\= q^{ \frac{1}{3} . \frac{1}{4} }= q^{\frac{1}{12}}\\=\sqrt[12]{ q }\\---------------\)
6. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
7. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-3}{4}}\\= x^{ \frac{-5}{2} . (\frac{-3}{4}) }= x^{\frac{15}{8}}\\=\sqrt[8]{ x^{15} }=|x|.\sqrt[8]{ x^{7} }\\---------------\)
8. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-4}{3}}\\= q^{ \frac{-5}{2} . (\frac{-4}{3}) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
9. \(\left(y^{\frac{4}{3}}\right)^{\frac{-4}{5}}\\= y^{ \frac{4}{3} . (\frac{-4}{5}) }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
10. \(\left(q^{\frac{5}{4}}\right)^{\frac{1}{2}}\\= q^{ \frac{5}{4} . \frac{1}{2} }= q^{\frac{5}{8}}\\=\sqrt[8]{ q^{5} }\\---------------\)
11. \(\left(x^{\frac{-5}{3}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-5}{3} . (\frac{-5}{6}) }= x^{\frac{25}{18}}\\=\sqrt[18]{ x^{25} }=|x|.\sqrt[18]{ x^{7} }\\---------------\)
12. \(\left(y^{-1}\right)^{\frac{-3}{2}}\\= y^{ -1 . (\frac{-3}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)