Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{3}}}{q^{-1}}\\= q^{ \frac{5}{3} - (-1) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{4} - \frac{1}{3} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{3} - \frac{3}{5} }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-5}{3}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
5. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-5}{6} - (\frac{-3}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
6. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{1}{3}}}\\= a^{ \frac{-1}{2} - \frac{1}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}. \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
7. \(\dfrac{x^{-2}}{x^{\frac{-4}{3}}}\\= x^{ -2 - (\frac{-4}{3}) }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
8. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-2}{3} - \frac{2}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
9. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-5}{2} - \frac{1}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
10. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{1}{2}}}\\= x^{ \frac{5}{4} - \frac{1}{2} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{-5}{6}}}{y^{2}}\\= y^{ \frac{-5}{6} - 2 }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
12. \(\dfrac{a^{\frac{1}{3}}}{a^{2}}\\= a^{ \frac{1}{3} - 2 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)