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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{\frac{2}{3}}\right)^{-1}\\= q^{ \frac{2}{3} . (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
2. \(\left(y^{1}\right)^{\frac{5}{2}}\\= y^{ 1 . \frac{5}{2} }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
3. \(\left(x^{-2}\right)^{\frac{1}{5}}\\= x^{ -2 . \frac{1}{5} }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
4. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{3}}\\= q^{ \frac{-1}{2} . \frac{5}{3} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
5. \(\left(x^{\frac{3}{4}}\right)^{\frac{-2}{3}}\\= x^{ \frac{3}{4} . (\frac{-2}{3}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
6. \(\left(q^{\frac{5}{2}}\right)^{\frac{2}{3}}\\= q^{ \frac{5}{2} . \frac{2}{3} }= q^{\frac{5}{3}}\\=\sqrt[3]{ q^{5} }=q.\sqrt[3]{ q^{2} }\\---------------\)
7. \(\left(q^{\frac{2}{3}}\right)^{\frac{-1}{5}}\\= q^{ \frac{2}{3} . (\frac{-1}{5}) }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
8. \(\left(y^{\frac{5}{2}}\right)^{\frac{-3}{5}}\\= y^{ \frac{5}{2} . (\frac{-3}{5}) }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
9. \(\left(y^{\frac{2}{5}}\right)^{\frac{1}{3}}\\= y^{ \frac{2}{5} . \frac{1}{3} }= y^{\frac{2}{15}}\\=\sqrt[15]{ y^{2} }\\---------------\)
10. \(\left(a^{-1}\right)^{\frac{-3}{2}}\\= a^{ -1 . (\frac{-3}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
11. \(\left(a^{\frac{1}{5}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{5} . (\frac{-3}{4}) }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
12. \(\left(q^{\frac{-4}{3}}\right)^{1}\\= q^{ \frac{-4}{3} . 1 }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)