Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{3}{2}}}\\= q^{ \frac{-3}{2} - \frac{3}{2} }= q^{-3}\\=\frac{1}{q^{3}}\\---------------\)
2. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{5}{3}}}\\= a^{ \frac{5}{2} - \frac{5}{3} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
3. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{5} - \frac{2}{3} }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{1}{2}}}\\= x^{ 1 - \frac{1}{2} }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
5. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-1}{5} - \frac{2}{3} }= x^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ x^{13} }}=\frac{1}{\sqrt[15]{ x^{13} }}. \color{purple}{\frac{\sqrt[15]{ x^{2} }}{\sqrt[15]{ x^{2} }}} \\=\frac{\sqrt[15]{ x^{2} }}{x}\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{-1}}\\= a^{ \frac{3}{5} - (-1) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
7. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{1}{3} - \frac{5}{3} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{3}{4}}}\\= x^{ \frac{5}{6} - \frac{3}{4} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)
10. \(\dfrac{q^{\frac{4}{5}}}{q^{1}}\\= q^{ \frac{4}{5} - 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
11. \(\dfrac{x^{\frac{-2}{5}}}{x^{1}}\\= x^{ \frac{-2}{5} - 1 }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-3}{5} - \frac{2}{3} }= y^{\frac{-19}{15}}\\=\frac{1}{\sqrt[15]{ y^{19} }}\\=\frac{1}{y.\sqrt[15]{ y^{4} }}=\frac{1}{y.\sqrt[15]{ y^{4} }} \color{purple}{\frac{\sqrt[15]{ y^{11} }}{\sqrt[15]{ y^{11} }}} \\=\frac{\sqrt[15]{ y^{11} }}{y^{2}}\\---------------\)