Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-1}{6} - \frac{3}{2} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{4}{3}}}\\= y^{ -1 - \frac{4}{3} }= y^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ y^{7} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y }}=\frac{1}{y^{2}.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{3}}\\---------------\)
3. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{3} - \frac{5}{3} }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
4. \(\dfrac{q^{2}}{q^{-2}}\\= q^{ 2 - (-2) }= q^{4}\\\\---------------\)
5. \(\dfrac{y^{-1}}{y^{\frac{5}{3}}}\\= y^{ -1 - \frac{5}{3} }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-5}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
7. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{-5}{3} - (\frac{-3}{4}) }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{2} - \frac{2}{3} }= x^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ x^{7} }}\\=\frac{1}{|x|.\sqrt[6]{ x }}=\frac{1}{|x|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{y^{1}}{y^{\frac{-1}{2}}}\\= y^{ 1 - (\frac{-1}{2}) }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{4} - \frac{1}{3} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
11. \(\dfrac{y^{1}}{y^{\frac{-1}{3}}}\\= y^{ 1 - (\frac{-1}{3}) }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)
12. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{2}{3}}}\\= a^{ \frac{3}{5} - \frac{2}{3} }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)