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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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