Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-5}{2} - (\frac{-4}{5}) }= y^{\frac{-17}{10}}\\=\frac{1}{\sqrt[10]{ y^{17} }}\\=\frac{1}{|y|.\sqrt[10]{ y^{7} }}=\frac{1}{|y|.\sqrt[10]{ y^{7} }} \color{purple}{\frac{\sqrt[10]{ y^{3} }}{\sqrt[10]{ y^{3} }}} \\=\frac{\sqrt[10]{ y^{3} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{1}{3} - (\frac{-1}{2}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
3. \(\dfrac{x^{\frac{5}{4}}}{x^{-1}}\\= x^{ \frac{5}{4} - (-1) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-2}{5}) }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{3} - \frac{3}{2} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
7. \(\dfrac{a^{2}}{a^{\frac{-1}{3}}}\\= a^{ 2 - (\frac{-1}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
8. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{4}{5}}}\\= q^{ \frac{3}{5} - \frac{4}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
9. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{1}{5} - (\frac{-1}{6}) }= a^{\frac{11}{30}}\\=\sqrt[30]{ a^{11} }\\---------------\)
10. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{4} - (\frac{-1}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-2}{5} - \frac{5}{4} }= x^{\frac{-33}{20}}\\=\frac{1}{\sqrt[20]{ x^{33} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{13} }}=\frac{1}{|x|.\sqrt[20]{ x^{13} }} \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-3}{2}}}{x^{\frac{-4}{3}}}\\= x^{ \frac{-3}{2} - (\frac{-4}{3}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)