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Werk uit m.b.v. de rekenregels

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

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