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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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