Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{1}{2} - (\frac{-3}{2}) }= a^{2}\\\\---------------\)
2. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-5}{3} - \frac{1}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{-5}{3}}}{x^{-1}}\\= x^{ \frac{-5}{3} - (-1) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
4. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-4}{3} - \frac{1}{2} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{4}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-5}{4} - \frac{2}{5} }= x^{\frac{-33}{20}}\\=\frac{1}{\sqrt[20]{ x^{33} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{13} }}=\frac{1}{|x|.\sqrt[20]{ x^{13} }} \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x^{2}|}\\---------------\)
6. \(\dfrac{q^{1}}{q^{\frac{5}{3}}}\\= q^{ 1 - \frac{5}{3} }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-3}{5}) }= a^{\frac{1}{10}}\\=\sqrt[10]{ a }\\---------------\)
8. \(\dfrac{a^{-2}}{a^{\frac{2}{5}}}\\= a^{ -2 - \frac{2}{5} }= a^{\frac{-12}{5}}\\=\frac{1}{\sqrt[5]{ a^{12} }}\\=\frac{1}{a^{2}.\sqrt[5]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{3}}\\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{4}{3} - \frac{4}{3} }= a^{0}\\=1\\---------------\)
10. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
11. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{3}{2} - (\frac{-3}{5}) }= x^{\frac{21}{10}}\\=\sqrt[10]{ x^{21} }=|x^{2}|.\sqrt[10]{ x }\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{1}{2}}}\\= q^{ 1 - \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)