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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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