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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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