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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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