Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{5}}}{q^{-2}}\\= q^{ \frac{-3}{5} - (-2) }= q^{\frac{7}{5}}\\=\sqrt[5]{ q^{7} }=q.\sqrt[5]{ q^{2} }\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{-1}{4}}}\\= a^{ -1 - (\frac{-1}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-1}{3} - (\frac{-2}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
4. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{4} - (\frac{-4}{5}) }= x^{\frac{41}{20}}\\=\sqrt[20]{ x^{41} }=|x^{2}|.\sqrt[20]{ x }\\---------------\)
5. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
6. \(\dfrac{y^{-1}}{y^{\frac{2}{3}}}\\= y^{ -1 - \frac{2}{3} }= y^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ y^{5} }}\\=\frac{1}{y.\sqrt[3]{ y^{2} }}=\frac{1}{y.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{2}}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-4}{5}}}\\= a^{ -1 - (\frac{-4}{5}) }= a^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ a }}=\frac{1}{\sqrt[5]{ a }}. \color{purple}{\frac{\sqrt[5]{ a^{4} }}{\sqrt[5]{ a^{4} }}} \\=\frac{\sqrt[5]{ a^{4} }}{a}\\---------------\)
8. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{4} - (\frac{-5}{3}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
9. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{2}{3} - (\frac{-1}{4}) }= a^{\frac{11}{12}}\\=\sqrt[12]{ a^{11} }\\---------------\)
10. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{3} - \frac{4}{5} }= x^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ x^{17} }}\\=\frac{1}{x.\sqrt[15]{ x^{2} }}=\frac{1}{x.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{1}{5}}}{y^{1}}\\= y^{ \frac{1}{5} - 1 }= y^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ y^{4} }}=\frac{1}{\sqrt[5]{ y^{4} }}. \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y}\\---------------\)
12. \(\dfrac{a^{\frac{-2}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-2}{5} - (\frac{-1}{3}) }= a^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ a }}=\frac{1}{\sqrt[15]{ a }}. \color{purple}{\frac{\sqrt[15]{ a^{14} }}{\sqrt[15]{ a^{14} }}} \\=\frac{\sqrt[15]{ a^{14} }}{a}\\---------------\)