Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{-3}{2}}}\\= q^{ -1 - (\frac{-3}{2}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
2. \(\dfrac{y^{\frac{-5}{6}}}{y^{-1}}\\= y^{ \frac{-5}{6} - (-1) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
3. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{2}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
4. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{-2}{5} - (\frac{-2}{5}) }= x^{0}\\=1\\---------------\)
5. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-2}{5} - \frac{5}{2} }= y^{\frac{-29}{10}}\\=\frac{1}{\sqrt[10]{ y^{29} }}\\=\frac{1}{|y^{2}|.\sqrt[10]{ y^{9} }}=\frac{1}{|y^{2}|.\sqrt[10]{ y^{9} }} \color{purple}{\frac{\sqrt[10]{ y }}{\sqrt[10]{ y }}} \\=\frac{\sqrt[10]{ y }}{|y^{3}|}\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
7. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-4}{5} - (\frac{-1}{2}) }= y^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ y^{3} }}=\frac{1}{\sqrt[10]{ y^{3} }}. \color{purple}{\frac{\sqrt[10]{ y^{7} }}{\sqrt[10]{ y^{7} }}} \\=\frac{\sqrt[10]{ y^{7} }}{|y|}\\---------------\)
8. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-4}{5}}}\\= q^{ \frac{5}{6} - (\frac{-4}{5}) }= q^{\frac{49}{30}}\\=\sqrt[30]{ q^{49} }=|q|.\sqrt[30]{ q^{19} }\\---------------\)
9. \(\dfrac{x^{\frac{-5}{3}}}{x^{1}}\\= x^{ \frac{-5}{3} - 1 }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
10. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-5}{4} - (\frac{-1}{6}) }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-2}{3} - \frac{1}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-4}{5} - \frac{5}{2} }= a^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ a^{33} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{4}|}\\---------------\)