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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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