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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{3}{4}}\right)^{\frac{-5}{4}}\\= a^{ \frac{3}{4} . (\frac{-5}{4}) }= a^{\frac{-15}{16}}\\=\frac{1}{\sqrt[16]{ a^{15} }}=\frac{1}{\sqrt[16]{ a^{15} }}. \color{purple}{\frac{\sqrt[16]{ a }}{\sqrt[16]{ a }}} \\=\frac{\sqrt[16]{ a }}{|a|}\\---------------\)
2. \(\left(x^{\frac{-5}{2}}\right)^{\frac{-1}{4}}\\= x^{ \frac{-5}{2} . (\frac{-1}{4}) }= x^{\frac{5}{8}}\\=\sqrt[8]{ x^{5} }\\---------------\)
3. \(\left(q^{\frac{-5}{2}}\right)^{\frac{-4}{5}}\\= q^{ \frac{-5}{2} . (\frac{-4}{5}) }= q^{2}\\\\---------------\)
4. \(\left(a^{\frac{-5}{6}}\right)^{\frac{-4}{5}}\\= a^{ \frac{-5}{6} . (\frac{-4}{5}) }= a^{\frac{2}{3}}\\=\sqrt[3]{ a^{2} }\\---------------\)
5. \(\left(x^{\frac{3}{5}}\right)^{\frac{5}{4}}\\= x^{ \frac{3}{5} . \frac{5}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
6. \(\left(a^{\frac{5}{4}}\right)^{\frac{1}{3}}\\= a^{ \frac{5}{4} . \frac{1}{3} }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
7. \(\left(a^{-1}\right)^{2}\\= a^{ -1 . 2 }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
8. \(\left(x^{\frac{1}{4}}\right)^{-2}\\= x^{ \frac{1}{4} . (-2) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
9. \(\left(x^{\frac{-5}{3}}\right)^{-1}\\= x^{ \frac{-5}{3} . (-1) }= x^{\frac{5}{3}}\\=\sqrt[3]{ x^{5} }=x.\sqrt[3]{ x^{2} }\\---------------\)
10. \(\left(q^{2}\right)^{\frac{3}{2}}\\= q^{ 2 . \frac{3}{2} }= q^{3}\\\\---------------\)
11. \(\left(x^{\frac{-1}{2}}\right)^{\frac{-1}{3}}\\= x^{ \frac{-1}{2} . (\frac{-1}{3}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
12. \(\left(q^{\frac{-1}{3}}\right)^{\frac{1}{5}}\\= q^{ \frac{-1}{3} . \frac{1}{5} }= q^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ q }}=\frac{1}{\sqrt[15]{ q }}. \color{purple}{\frac{\sqrt[15]{ q^{14} }}{\sqrt[15]{ q^{14} }}} \\=\frac{\sqrt[15]{ q^{14} }}{q}\\---------------\)