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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-3}{5}}\right)^{\frac{-5}{3}}\\= x^{ \frac{-3}{5} . (\frac{-5}{3}) }= x^{1}\\\\---------------\)
2. \(\left(y^{\frac{1}{4}}\right)^{1}\\= y^{ \frac{1}{4} . 1 }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
3. \(\left(x^{-1}\right)^{\frac{5}{3}}\\= x^{ -1 . \frac{5}{3} }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
4. \(\left(y^{\frac{3}{4}}\right)^{-1}\\= y^{ \frac{3}{4} . (-1) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
5. \(\left(q^{\frac{-5}{2}}\right)^{\frac{1}{2}}\\= q^{ \frac{-5}{2} . \frac{1}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
6. \(\left(y^{\frac{1}{6}}\right)^{2}\\= y^{ \frac{1}{6} . 2 }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
7. \(\left(q^{\frac{-4}{5}}\right)^{\frac{2}{3}}\\= q^{ \frac{-4}{5} . \frac{2}{3} }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
8. \(\left(q^{\frac{-4}{3}}\right)^{\frac{5}{4}}\\= q^{ \frac{-4}{3} . \frac{5}{4} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
9. \(\left(a^{-1}\right)^{\frac{1}{2}}\\= a^{ -1 . \frac{1}{2} }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
10. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= y^{ \frac{-4}{5} . (\frac{-1}{2}) }= y^{\frac{2}{5}}\\=\sqrt[5]{ y^{2} }\\---------------\)
11. \(\left(a^{\frac{1}{3}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{3} . (\frac{-1}{5}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)
12. \(\left(q^{\frac{1}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{1}{2} . (\frac{-5}{4}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)