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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{4}}\right)^{\frac{4}{5}}\\= y^{ \frac{1}{4} . \frac{4}{5} }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
2. \(\left(y^{\frac{1}{2}}\right)^{1}\\= y^{ \frac{1}{2} . 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\left(x^{\frac{-1}{4}}\right)^{-2}\\= x^{ \frac{-1}{4} . (-2) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
4. \(\left(q^{\frac{2}{3}}\right)^{\frac{-3}{4}}\\= q^{ \frac{2}{3} . (\frac{-3}{4}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
5. \(\left(y^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{2} . (\frac{-2}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
6. \(\left(x^{\frac{-1}{5}}\right)^{\frac{4}{5}}\\= x^{ \frac{-1}{5} . \frac{4}{5} }= x^{\frac{-4}{25}}\\=\frac{1}{\sqrt[25]{ x^{4} }}=\frac{1}{\sqrt[25]{ x^{4} }}. \color{purple}{\frac{\sqrt[25]{ x^{21} }}{\sqrt[25]{ x^{21} }}} \\=\frac{\sqrt[25]{ x^{21} }}{x}\\---------------\)
7. \(\left(a^{\frac{5}{2}}\right)^{\frac{-4}{3}}\\= a^{ \frac{5}{2} . (\frac{-4}{3}) }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
8. \(\left(x^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= x^{ \frac{-5}{6} . \frac{1}{2} }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
9. \(\left(q^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= q^{ \frac{1}{2} . \frac{5}{6} }= q^{\frac{5}{12}}\\=\sqrt[12]{ q^{5} }\\---------------\)
10. \(\left(a^{\frac{-2}{5}}\right)^{\frac{5}{2}}\\= a^{ \frac{-2}{5} . \frac{5}{2} }= a^{-1}\\=\frac{1}{a}\\---------------\)
11. \(\left(y^{\frac{-2}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{-2}{5} . \frac{1}{3} }= y^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ y^{2} }}=\frac{1}{\sqrt[15]{ y^{2} }}. \color{purple}{\frac{\sqrt[15]{ y^{13} }}{\sqrt[15]{ y^{13} }}} \\=\frac{\sqrt[15]{ y^{13} }}{y}\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{-2}{3}}\\= q^{ \frac{1}{2} . (\frac{-2}{3}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)