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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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