Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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