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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-4}{3}}\right)^{2}\\= x^{ \frac{-4}{3} . 2 }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
2. \(\left(y^{\frac{-1}{6}}\right)^{\frac{-1}{6}}\\= y^{ \frac{-1}{6} . (\frac{-1}{6}) }= y^{\frac{1}{36}}\\=\sqrt[36]{ y }\\---------------\)
3. \(\left(x^{\frac{-2}{5}}\right)^{1}\\= x^{ \frac{-2}{5} . 1 }= x^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ x^{2} }}=\frac{1}{\sqrt[5]{ x^{2} }}. \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x}\\---------------\)
4. \(\left(a^{\frac{-4}{3}}\right)^{-1}\\= a^{ \frac{-4}{3} . (-1) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
5. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-2}{3} . (\frac{-2}{3}) }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
6. \(\left(y^{2}\right)^{\frac{5}{6}}\\= y^{ 2 . \frac{5}{6} }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
7. \(\left(a^{1}\right)^{1}\\= a^{ 1 . 1 }= a^{1}\\\\---------------\)
8. \(\left(a^{\frac{3}{4}}\right)^{\frac{3}{5}}\\= a^{ \frac{3}{4} . \frac{3}{5} }= a^{\frac{9}{20}}\\=\sqrt[20]{ a^{9} }\\---------------\)
9. \(\left(x^{\frac{1}{3}}\right)^{\frac{2}{5}}\\= x^{ \frac{1}{3} . \frac{2}{5} }= x^{\frac{2}{15}}\\=\sqrt[15]{ x^{2} }\\---------------\)
10. \(\left(q^{\frac{1}{4}}\right)^{\frac{3}{2}}\\= q^{ \frac{1}{4} . \frac{3}{2} }= q^{\frac{3}{8}}\\=\sqrt[8]{ q^{3} }\\---------------\)
11. \(\left(a^{\frac{4}{5}}\right)^{\frac{1}{4}}\\= a^{ \frac{4}{5} . \frac{1}{4} }= a^{\frac{1}{5}}\\=\sqrt[5]{ a }\\---------------\)
12. \(\left(x^{\frac{2}{5}}\right)^{\frac{1}{2}}\\= x^{ \frac{2}{5} . \frac{1}{2} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)