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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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