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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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