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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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