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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{-1}\\= y^{ -1 . (-1) }= y^{1}\\\\---------------\)
2. \(\left(a^{\frac{-5}{6}}\right)^{\frac{5}{4}}\\= a^{ \frac{-5}{6} . \frac{5}{4} }= a^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ a^{25} }}\\=\frac{1}{|a|.\sqrt[24]{ a }}=\frac{1}{|a|.\sqrt[24]{ a }} \color{purple}{\frac{\sqrt[24]{ a^{23} }}{\sqrt[24]{ a^{23} }}} \\=\frac{\sqrt[24]{ a^{23} }}{|a^{2}|}\\---------------\)
3. \(\left(x^{\frac{-1}{4}}\right)^{\frac{-1}{5}}\\= x^{ \frac{-1}{4} . (\frac{-1}{5}) }= x^{\frac{1}{20}}\\=\sqrt[20]{ x }\\---------------\)
4. \(\left(q^{\frac{2}{3}}\right)^{\frac{3}{5}}\\= q^{ \frac{2}{3} . \frac{3}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
5. \(\left(y^{\frac{-1}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-1}{5} . (\frac{-2}{3}) }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
6. \(\left(y^{\frac{5}{2}}\right)^{\frac{1}{3}}\\= y^{ \frac{5}{2} . \frac{1}{3} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
7. \(\left(a^{2}\right)^{\frac{1}{3}}\\= a^{ 2 . \frac{1}{3} }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
8. \(\left(q^{\frac{-3}{4}}\right)^{\frac{3}{4}}\\= q^{ \frac{-3}{4} . \frac{3}{4} }= q^{\frac{-9}{16}}\\=\frac{1}{\sqrt[16]{ q^{9} }}=\frac{1}{\sqrt[16]{ q^{9} }}. \color{purple}{\frac{\sqrt[16]{ q^{7} }}{\sqrt[16]{ q^{7} }}} \\=\frac{\sqrt[16]{ q^{7} }}{|q|}\\---------------\)
9. \(\left(q^{\frac{1}{3}}\right)^{\frac{-1}{2}}\\= q^{ \frac{1}{3} . (\frac{-1}{2}) }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
10. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\left(y^{-2}\right)^{-1}\\= y^{ -2 . (-1) }= y^{2}\\\\---------------\)
12. \(\left(a^{1}\right)^{\frac{4}{3}}\\= a^{ 1 . \frac{4}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)