Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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