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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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