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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{1}\right)^{\frac{3}{4}}\\= a^{ 1 . \frac{3}{4} }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
2. \(\left(a^{\frac{4}{3}}\right)^{\frac{-4}{3}}\\= a^{ \frac{4}{3} . (\frac{-4}{3}) }= a^{\frac{-16}{9}}\\=\frac{1}{\sqrt[9]{ a^{16} }}\\=\frac{1}{a.\sqrt[9]{ a^{7} }}=\frac{1}{a.\sqrt[9]{ a^{7} }} \color{purple}{\frac{\sqrt[9]{ a^{2} }}{\sqrt[9]{ a^{2} }}} \\=\frac{\sqrt[9]{ a^{2} }}{a^{2}}\\---------------\)
3. \(\left(q^{\frac{-5}{2}}\right)^{\frac{4}{5}}\\= q^{ \frac{-5}{2} . \frac{4}{5} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
4. \(\left(y^{\frac{-5}{2}}\right)^{\frac{4}{3}}\\= y^{ \frac{-5}{2} . \frac{4}{3} }= y^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ y^{10} }}\\=\frac{1}{y^{3}.\sqrt[3]{ y }}=\frac{1}{y^{3}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{4}}\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= q^{ \frac{-1}{2} . (\frac{-5}{2}) }= q^{\frac{5}{4}}\\=\sqrt[4]{ q^{5} }=|q|.\sqrt[4]{ q }\\---------------\)
6. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-5}{2} . (\frac{-5}{6}) }= x^{\frac{25}{12}}\\=\sqrt[12]{ x^{25} }=|x^{2}|.\sqrt[12]{ x }\\---------------\)
7. \(\left(x^{1}\right)^{\frac{-5}{2}}\\= x^{ 1 . (\frac{-5}{2}) }= x^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ x^{5} } }\\=\frac{1}{|x^{2}|. \sqrt{ x } }=\frac{1}{|x^{2}|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{3}|}\\---------------\)
8. \(\left(y^{\frac{-4}{5}}\right)^{\frac{-5}{6}}\\= y^{ \frac{-4}{5} . (\frac{-5}{6}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
9. \(\left(a^{\frac{4}{3}}\right)^{\frac{1}{3}}\\= a^{ \frac{4}{3} . \frac{1}{3} }= a^{\frac{4}{9}}\\=\sqrt[9]{ a^{4} }\\---------------\)
10. \(\left(q^{\frac{1}{2}}\right)^{\frac{-3}{4}}\\= q^{ \frac{1}{2} . (\frac{-3}{4}) }= q^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ q^{3} }}=\frac{1}{\sqrt[8]{ q^{3} }}. \color{purple}{\frac{\sqrt[8]{ q^{5} }}{\sqrt[8]{ q^{5} }}} \\=\frac{\sqrt[8]{ q^{5} }}{|q|}\\---------------\)
11. \(\left(y^{1}\right)^{\frac{1}{2}}\\= y^{ 1 . \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
12. \(\left(y^{-1}\right)^{\frac{5}{2}}\\= y^{ -1 . \frac{5}{2} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)