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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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