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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(x^{\frac{-4}{5}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-4}{5} . (\frac{-1}{2}) }= x^{\frac{2}{5}}\\=\sqrt[5]{ x^{2} }\\---------------\)
2. \(\left(x^{\frac{-1}{5}}\right)^{\frac{-5}{4}}\\= x^{ \frac{-1}{5} . (\frac{-5}{4}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
3. \(\left(q^{\frac{3}{4}}\right)^{\frac{-5}{6}}\\= q^{ \frac{3}{4} . (\frac{-5}{6}) }= q^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ q^{5} }}=\frac{1}{\sqrt[8]{ q^{5} }}. \color{purple}{\frac{\sqrt[8]{ q^{3} }}{\sqrt[8]{ q^{3} }}} \\=\frac{\sqrt[8]{ q^{3} }}{|q|}\\---------------\)
4. \(\left(q^{\frac{5}{2}}\right)^{\frac{5}{4}}\\= q^{ \frac{5}{2} . \frac{5}{4} }= q^{\frac{25}{8}}\\=\sqrt[8]{ q^{25} }=|q^{3}|.\sqrt[8]{ q }\\---------------\)
5. \(\left(q^{\frac{5}{2}}\right)^{\frac{-5}{4}}\\= q^{ \frac{5}{2} . (\frac{-5}{4}) }= q^{\frac{-25}{8}}\\=\frac{1}{\sqrt[8]{ q^{25} }}\\=\frac{1}{|q^{3}|.\sqrt[8]{ q }}=\frac{1}{|q^{3}|.\sqrt[8]{ q }} \color{purple}{\frac{\sqrt[8]{ q^{7} }}{\sqrt[8]{ q^{7} }}} \\=\frac{\sqrt[8]{ q^{7} }}{|q^{4}|}\\---------------\)
6. \(\left(a^{\frac{-4}{3}}\right)^{2}\\= a^{ \frac{-4}{3} . 2 }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
7. \(\left(y^{\frac{-1}{3}}\right)^{\frac{4}{5}}\\= y^{ \frac{-1}{3} . \frac{4}{5} }= y^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ y^{4} }}=\frac{1}{\sqrt[15]{ y^{4} }}. \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y}\\---------------\)
8. \(\left(a^{\frac{-3}{2}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{2} . \frac{5}{4} }= a^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ a^{15} }}\\=\frac{1}{|a|.\sqrt[8]{ a^{7} }}=\frac{1}{|a|.\sqrt[8]{ a^{7} }} \color{purple}{\frac{\sqrt[8]{ a }}{\sqrt[8]{ a }}} \\=\frac{\sqrt[8]{ a }}{|a^{2}|}\\---------------\)
9. \(\left(y^{\frac{4}{3}}\right)^{\frac{-4}{5}}\\= y^{ \frac{4}{3} . (\frac{-4}{5}) }= y^{\frac{-16}{15}}\\=\frac{1}{\sqrt[15]{ y^{16} }}\\=\frac{1}{y.\sqrt[15]{ y }}=\frac{1}{y.\sqrt[15]{ y }} \color{purple}{\frac{\sqrt[15]{ y^{14} }}{\sqrt[15]{ y^{14} }}} \\=\frac{\sqrt[15]{ y^{14} }}{y^{2}}\\---------------\)
10. \(\left(q^{1}\right)^{\frac{-2}{3}}\\= q^{ 1 . (\frac{-2}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
11. \(\left(a^{\frac{2}{3}}\right)^{\frac{-5}{4}}\\= a^{ \frac{2}{3} . (\frac{-5}{4}) }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
12. \(\left(a^{\frac{1}{3}}\right)^{\frac{-3}{4}}\\= a^{ \frac{1}{3} . (\frac{-3}{4}) }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)