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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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