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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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