Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{1}{5}}}\\= y^{ \frac{-5}{6} - \frac{1}{5} }= y^{\frac{-31}{30}}\\=\frac{1}{\sqrt[30]{ y^{31} }}\\=\frac{1}{|y|.\sqrt[30]{ y }}=\frac{1}{|y|.\sqrt[30]{ y }} \color{purple}{\frac{\sqrt[30]{ y^{29} }}{\sqrt[30]{ y^{29} }}} \\=\frac{\sqrt[30]{ y^{29} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-1}{2} - \frac{4}{3} }= y^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[6]{ y^{5} }}=\frac{1}{|y|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{5}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{5}) }= a^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ a }}=\frac{1}{\sqrt[10]{ a }}. \color{purple}{\frac{\sqrt[10]{ a^{9} }}{\sqrt[10]{ a^{9} }}} \\=\frac{\sqrt[10]{ a^{9} }}{|a|}\\---------------\)
4. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{5}{3} - \frac{4}{3} }= a^{\frac{1}{3}}\\=\sqrt[3]{ a }\\---------------\)
5. \(\dfrac{a^{1}}{a^{\frac{-2}{5}}}\\= a^{ 1 - (\frac{-2}{5}) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
6. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-5}{2} - \frac{4}{5} }= x^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ x^{33} }}\\=\frac{1}{|x^{3}|.\sqrt[10]{ x^{3} }}=\frac{1}{|x^{3}|.\sqrt[10]{ x^{3} }} \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x^{4}|}\\---------------\)
7. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{4}}}\\= a^{ \frac{1}{2} - \frac{1}{4} }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{4}{5} - (\frac{-3}{5}) }= x^{\frac{7}{5}}\\=\sqrt[5]{ x^{7} }=x.\sqrt[5]{ x^{2} }\\---------------\)
9. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{4}{5}}}\\= q^{ \frac{5}{6} - \frac{4}{5} }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{5} - \frac{1}{2} }= x^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ x^{7} }}=\frac{1}{\sqrt[10]{ x^{7} }}. \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x|}\\---------------\)
11. \(\dfrac{y^{-1}}{y^{\frac{-1}{3}}}\\= y^{ -1 - (\frac{-1}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
12. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{3}{4}}}\\= q^{ \frac{-5}{6} - \frac{3}{4} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)