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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\left(a^{\frac{-3}{5}}\right)^{2}\\= a^{ \frac{-3}{5} . 2 }= a^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ a^{6} }}\\=\frac{1}{a.\sqrt[5]{ a }}=\frac{1}{a.\sqrt[5]{ a }} \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a^{2}}\\---------------\)
2. \(\left(x^{1}\right)^{\frac{-5}{4}}\\= x^{ 1 . (\frac{-5}{4}) }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
3. \(\left(y^{\frac{5}{3}}\right)^{\frac{-3}{4}}\\= y^{ \frac{5}{3} . (\frac{-3}{4}) }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
4. \(\left(q^{\frac{1}{2}}\right)^{\frac{3}{5}}\\= q^{ \frac{1}{2} . \frac{3}{5} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
5. \(\left(y^{\frac{5}{4}}\right)^{\frac{-1}{3}}\\= y^{ \frac{5}{4} . (\frac{-1}{3}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
6. \(\left(x^{\frac{3}{5}}\right)^{1}\\= x^{ \frac{3}{5} . 1 }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
7. \(\left(y^{\frac{2}{3}}\right)^{-1}\\= y^{ \frac{2}{3} . (-1) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
8. \(\left(a^{\frac{5}{3}}\right)^{\frac{-2}{3}}\\= a^{ \frac{5}{3} . (\frac{-2}{3}) }= a^{\frac{-10}{9}}\\=\frac{1}{\sqrt[9]{ a^{10} }}\\=\frac{1}{a.\sqrt[9]{ a }}=\frac{1}{a.\sqrt[9]{ a }} \color{purple}{\frac{\sqrt[9]{ a^{8} }}{\sqrt[9]{ a^{8} }}} \\=\frac{\sqrt[9]{ a^{8} }}{a^{2}}\\---------------\)
9. \(\left(x^{1}\right)^{\frac{-4}{3}}\\= x^{ 1 . (\frac{-4}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
10. \(\left(y^{\frac{-3}{5}}\right)^{\frac{-4}{5}}\\= y^{ \frac{-3}{5} . (\frac{-4}{5}) }= y^{\frac{12}{25}}\\=\sqrt[25]{ y^{12} }\\---------------\)
11. \(\left(q^{1}\right)^{\frac{2}{3}}\\= q^{ 1 . \frac{2}{3} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
12. \(\left(y^{-1}\right)^{1}\\= y^{ -1 . 1 }= y^{-1}\\=\frac{1}{y}\\---------------\)