Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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