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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{1}{2}}\right)^{\frac{5}{6}}\\= x^{ \frac{1}{2} . \frac{5}{6} }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
2. \(\left(a^{\frac{-5}{4}}\right)^{-1}\\= a^{ \frac{-5}{4} . (-1) }= a^{\frac{5}{4}}\\=\sqrt[4]{ a^{5} }=|a|.\sqrt[4]{ a }\\---------------\)
3. \(\left(y^{\frac{-5}{3}}\right)^{\frac{5}{3}}\\= y^{ \frac{-5}{3} . \frac{5}{3} }= y^{\frac{-25}{9}}\\=\frac{1}{\sqrt[9]{ y^{25} }}\\=\frac{1}{y^{2}.\sqrt[9]{ y^{7} }}=\frac{1}{y^{2}.\sqrt[9]{ y^{7} }} \color{purple}{\frac{\sqrt[9]{ y^{2} }}{\sqrt[9]{ y^{2} }}} \\=\frac{\sqrt[9]{ y^{2} }}{y^{3}}\\---------------\)
4. \(\left(y^{\frac{4}{3}}\right)^{\frac{1}{5}}\\= y^{ \frac{4}{3} . \frac{1}{5} }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
5. \(\left(x^{\frac{3}{2}}\right)^{\frac{3}{2}}\\= x^{ \frac{3}{2} . \frac{3}{2} }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
6. \(\left(q^{\frac{1}{2}}\right)^{\frac{-4}{5}}\\= q^{ \frac{1}{2} . (\frac{-4}{5}) }= q^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ q^{2} }}=\frac{1}{\sqrt[5]{ q^{2} }}. \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q}\\---------------\)
7. \(\left(a^{1}\right)^{\frac{5}{6}}\\= a^{ 1 . \frac{5}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
8. \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\left(q^{2}\right)^{2}\\= q^{ 2 . 2 }= q^{4}\\\\---------------\)
10. \(\left(y^{\frac{-4}{3}}\right)^{\frac{2}{3}}\\= y^{ \frac{-4}{3} . \frac{2}{3} }= y^{\frac{-8}{9}}\\=\frac{1}{\sqrt[9]{ y^{8} }}=\frac{1}{\sqrt[9]{ y^{8} }}. \color{purple}{\frac{\sqrt[9]{ y }}{\sqrt[9]{ y }}} \\=\frac{\sqrt[9]{ y }}{y}\\---------------\)
11. \(\left(q^{\frac{1}{2}}\right)^{-1}\\= q^{ \frac{1}{2} . (-1) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
12. \(\left(q^{\frac{5}{2}}\right)^{1}\\= q^{ \frac{5}{2} . 1 }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)