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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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