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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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