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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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