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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(y^{\frac{-3}{4}}\right)^{\frac{-5}{2}}\\= y^{ \frac{-3}{4} . (\frac{-5}{2}) }= y^{\frac{15}{8}}\\=\sqrt[8]{ y^{15} }=|y|.\sqrt[8]{ y^{7} }\\---------------\)
2. \(\left(q^{\frac{-3}{2}}\right)^{1}\\= q^{ \frac{-3}{2} . 1 }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
3. \(\left(y^{-2}\right)^{-1}\\= y^{ -2 . (-1) }= y^{2}\\\\---------------\)
4. \(\left(y^{\frac{-3}{4}}\right)^{\frac{1}{2}}\\= y^{ \frac{-3}{4} . \frac{1}{2} }= y^{\frac{-3}{8}}\\=\frac{1}{\sqrt[8]{ y^{3} }}=\frac{1}{\sqrt[8]{ y^{3} }}. \color{purple}{\frac{\sqrt[8]{ y^{5} }}{\sqrt[8]{ y^{5} }}} \\=\frac{\sqrt[8]{ y^{5} }}{|y|}\\---------------\)
5. \(\left(q^{\frac{-1}{2}}\right)^{\frac{5}{2}}\\= q^{ \frac{-1}{2} . \frac{5}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
6. \(\left(q^{\frac{-1}{2}}\right)^{\frac{1}{6}}\\= q^{ \frac{-1}{2} . \frac{1}{6} }= q^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ q }}=\frac{1}{\sqrt[12]{ q }}. \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q|}\\---------------\)
7. \(\left(a^{\frac{-3}{2}}\right)^{-1}\\= a^{ \frac{-3}{2} . (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
8. \(\left(y^{-2}\right)^{\frac{-1}{4}}\\= y^{ -2 . (\frac{-1}{4}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
9. \(\left(a^{\frac{1}{4}}\right)^{\frac{-1}{5}}\\= a^{ \frac{1}{4} . (\frac{-1}{5}) }= a^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ a }}=\frac{1}{\sqrt[20]{ a }}. \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a|}\\---------------\)
10. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{2}}\\= x^{ \frac{-1}{2} . (\frac{-1}{2}) }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)
11. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-5}{6}}\\= x^{ \frac{-1}{2} . (\frac{-5}{6}) }= x^{\frac{5}{12}}\\=\sqrt[12]{ x^{5} }\\---------------\)
12. \(\left(y^{1}\right)^{1}\\= y^{ 1 . 1 }= y^{1}\\\\---------------\)