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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{-1}\right)^{\frac{1}{5}}\\= y^{ -1 . \frac{1}{5} }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
2. \(\left(a^{\frac{3}{4}}\right)^{\frac{-1}{4}}\\= a^{ \frac{3}{4} . (\frac{-1}{4}) }= a^{\frac{-3}{16}}\\=\frac{1}{\sqrt[16]{ a^{3} }}=\frac{1}{\sqrt[16]{ a^{3} }}. \color{purple}{\frac{\sqrt[16]{ a^{13} }}{\sqrt[16]{ a^{13} }}} \\=\frac{\sqrt[16]{ a^{13} }}{|a|}\\---------------\)
3. \(\left(a^{\frac{2}{3}}\right)^{1}\\= a^{ \frac{2}{3} . 1 }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
4. \(\left(a^{\frac{2}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{2}{3} . (\frac{-4}{3}) }= a^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ a^{8} }}=\frac{1}{\sqrt[9]{ a^{8} }}. \color{purple}{\frac{\sqrt[9]{ a }}{\sqrt[9]{ a }}} \\=\frac{\sqrt[9]{ a }}{a}\\---------------\)
5. \(\left(a^{-2}\right)^{\frac{4}{3}}\\= a^{ -2 . \frac{4}{3} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
6. \(\left(x^{\frac{1}{2}}\right)^{\frac{4}{5}}\\= x^{ \frac{1}{2} . \frac{4}{5} }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
7. \(\left(q^{-1}\right)^{\frac{5}{3}}\\= q^{ -1 . \frac{5}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
8. \(\left(q^{\frac{-1}{4}}\right)^{-2}\\= q^{ \frac{-1}{4} . (-2) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\left(a^{\frac{5}{3}}\right)^{\frac{1}{2}}\\= a^{ \frac{5}{3} . \frac{1}{2} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
10. \(\left(x^{\frac{-1}{5}}\right)^{\frac{2}{3}}\\= x^{ \frac{-1}{5} . \frac{2}{3} }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
11. \(\left(q^{\frac{3}{5}}\right)^{\frac{5}{2}}\\= q^{ \frac{3}{5} . \frac{5}{2} }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
12. \(\left(x^{2}\right)^{1}\\= x^{ 2 . 1 }= x^{2}\\\\---------------\)