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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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