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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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