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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(q^{-1}\right)^{\frac{-3}{4}}\\= q^{ -1 . (\frac{-3}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
2. \(\left(x^{\frac{-1}{2}}\right)^{\frac{3}{5}}\\= x^{ \frac{-1}{2} . \frac{3}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
3. \(\left(q^{\frac{-5}{4}}\right)^{\frac{-2}{3}}\\= q^{ \frac{-5}{4} . (\frac{-2}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
4. \(\left(x^{\frac{-2}{3}}\right)^{\frac{-2}{3}}\\= x^{ \frac{-2}{3} . (\frac{-2}{3}) }= x^{\frac{4}{9}}\\=\sqrt[9]{ x^{4} }\\---------------\)
5. \(\left(a^{1}\right)^{\frac{2}{5}}\\= a^{ 1 . \frac{2}{5} }= a^{\frac{2}{5}}\\=\sqrt[5]{ a^{2} }\\---------------\)
6. \(\left(a^{\frac{-5}{3}}\right)^{\frac{2}{3}}\\= a^{ \frac{-5}{3} . \frac{2}{3} }= a^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ a^{10} }}\\=\frac{1}{a.\sqrt[9]{ a }}=\frac{1}{a.\sqrt[9]{ a }} \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a^{2}}\\---------------\)
7. \(\left(x^{\frac{2}{5}}\right)^{\frac{1}{4}}\\= x^{ \frac{2}{5} . \frac{1}{4} }= x^{\frac{1}{10}}\\=\sqrt[10]{ x }\\---------------\)
8. \(\left(y^{\frac{-2}{5}}\right)^{\frac{-2}{3}}\\= y^{ \frac{-2}{5} . (\frac{-2}{3}) }= y^{\frac{4}{15}}\\=\sqrt[15]{ y^{4} }\\---------------\)
9. \(\left(a^{\frac{-3}{4}}\right)^{\frac{-5}{2}}\\= a^{ \frac{-3}{4} . (\frac{-5}{2}) }= a^{\frac{15}{8}}\\=\sqrt[8]{ a^{15} }=|a|.\sqrt[8]{ a^{7} }\\---------------\)
10. \(\left(y^{\frac{-5}{6}}\right)^{\frac{1}{4}}\\= y^{ \frac{-5}{6} . \frac{1}{4} }= y^{\frac{-5}{24}}\\=\frac{1}{\sqrt[24]{ y^{5} }}=\frac{1}{\sqrt[24]{ y^{5} }}. \color{purple}{\frac{\sqrt[24]{ y^{19} }}{\sqrt[24]{ y^{19} }}} \\=\frac{\sqrt[24]{ y^{19} }}{|y|}\\---------------\)
11. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{2}}\\= x^{ \frac{-1}{2} . (\frac{-5}{2}) }= x^{\frac{5}{4}}\\=\sqrt[4]{ x^{5} }=|x|.\sqrt[4]{ x }\\---------------\)
12. \(\left(a^{1}\right)^{\frac{4}{3}}\\= a^{ 1 . \frac{4}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)