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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{1}{6}}\right)^{1}\\= y^{ \frac{1}{6} . 1 }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
2. \(\left(q^{\frac{-1}{5}}\right)^{\frac{5}{4}}\\= q^{ \frac{-1}{5} . \frac{5}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
3. \(\left(q^{2}\right)^{\frac{2}{3}}\\= q^{ 2 . \frac{2}{3} }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
4. \(\left(x^{-1}\right)^{\frac{3}{2}}\\= x^{ -1 . \frac{3}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
5. \(\left(a^{\frac{-5}{2}}\right)^{\frac{2}{3}}\\= a^{ \frac{-5}{2} . \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
6. \(\left(x^{\frac{-5}{3}}\right)^{\frac{4}{5}}\\= x^{ \frac{-5}{3} . \frac{4}{5} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
7. \(\left(q^{\frac{-1}{4}}\right)^{\frac{5}{4}}\\= q^{ \frac{-1}{4} . \frac{5}{4} }= q^{\frac{-5}{16}}\\=\frac{1}{\sqrt[16]{ q^{5} }}=\frac{1}{\sqrt[16]{ q^{5} }}. \color{purple}{\frac{\sqrt[16]{ q^{11} }}{\sqrt[16]{ q^{11} }}} \\=\frac{\sqrt[16]{ q^{11} }}{|q|}\\---------------\)
8. \(\left(y^{\frac{1}{2}}\right)^{\frac{-2}{5}}\\= y^{ \frac{1}{2} . (\frac{-2}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
9. \(\left(x^{\frac{1}{3}}\right)^{-1}\\= x^{ \frac{1}{3} . (-1) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
10. \(\left(y^{\frac{3}{5}}\right)^{-1}\\= y^{ \frac{3}{5} . (-1) }= y^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ y^{3} }}=\frac{1}{\sqrt[5]{ y^{3} }}. \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y}\\---------------\)
11. \(\left(q^{\frac{-5}{3}}\right)^{1}\\= q^{ \frac{-5}{3} . 1 }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
12. \(\left(a^{\frac{-3}{4}}\right)^{\frac{5}{4}}\\= a^{ \frac{-3}{4} . \frac{5}{4} }= a^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ a^{15} }}=\frac{1}{\sqrt[16]{ a^{15} }}. \color{purple}{\frac{\sqrt[16]{ a }}{\sqrt[16]{ a }}} \\=\frac{\sqrt[16]{ a }}{|a|}\\---------------\)