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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{5}}\right)^{1}\\= y^{ \frac{1}{5} . 1 }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
2. \(\left(q^{\frac{-2}{3}}\right)^{\frac{3}{4}}\\= q^{ \frac{-2}{3} . \frac{3}{4} }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
3. \(\left(q^{\frac{1}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{1}{4} . (\frac{-5}{6}) }= q^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ q^{5} }}=\frac{1}{\sqrt[24]{ q^{5} }}. \color{purple}{\frac{\sqrt[24]{ q^{19} }}{\sqrt[24]{ q^{19} }}} \\=\frac{\sqrt[24]{ q^{19} }}{|q|}\\---------------\)
4. \(\left(a^{-1}\right)^{\frac{1}{3}}\\= a^{ -1 . \frac{1}{3} }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
5. \(\left(x^{\frac{1}{3}}\right)^{1}\\= x^{ \frac{1}{3} . 1 }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
6. \(\left(y^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-1}{2} . (\frac{-1}{2}) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
7. \(\left(a^{\frac{-1}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{-1}{3} . \frac{1}{2} }= a^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ a }}=\frac{1}{\sqrt[6]{ a }}. \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a|}\\---------------\)
8. \(\left(x^{1}\right)^{2}\\= x^{ 1 . 2 }= x^{2}\\\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{-2}{5}}\\= a^{ -1 . (\frac{-2}{5}) }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
10. \(\left(a^{\frac{2}{3}}\right)^{-1}\\= a^{ \frac{2}{3} . (-1) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\left(a^{\frac{2}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{2}{5} . (\frac{-5}{4}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\left(q^{\frac{2}{5}}\right)^{\frac{-3}{2}}\\= q^{ \frac{2}{5} . (\frac{-3}{2}) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}. \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)