Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-5}{4} - (\frac{-2}{3}) }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
2. \(\dfrac{x^{\frac{-4}{3}}}{x^{\frac{5}{2}}}\\= x^{ \frac{-4}{3} - \frac{5}{2} }= x^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ x^{23} }}\\=\frac{1}{|x^{3}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{3}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{4}|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{1}{6} - (\frac{-2}{5}) }= q^{\frac{17}{30}}\\=\sqrt[30]{ q^{17} }\\---------------\)
4. \(\dfrac{q^{\frac{-3}{5}}}{q^{1}}\\= q^{ \frac{-3}{5} - 1 }= q^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ q^{8} }}\\=\frac{1}{q.\sqrt[5]{ q^{3} }}=\frac{1}{q.\sqrt[5]{ q^{3} }} \color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{2} - (\frac{-1}{3}) }= x^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ x^{13} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x }}=\frac{1}{|x^{2}|.\sqrt[6]{ x }} \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x^{3}|}\\---------------\)
6. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{1}{2} - (\frac{-1}{2}) }= y^{1}\\\\---------------\)
7. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-1}{6} - \frac{4}{5} }= q^{\frac{-29}{30}}\\=\frac{1}{\sqrt[30]{ q^{29} }}=\frac{1}{\sqrt[30]{ q^{29} }}. \color{purple}{\frac{\sqrt[30]{ q }}{\sqrt[30]{ q }}} \\=\frac{\sqrt[30]{ q }}{|q|}\\---------------\)
8. \(\dfrac{x^{\frac{-2}{5}}}{x^{\frac{2}{5}}}\\= x^{ \frac{-2}{5} - \frac{2}{5} }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{2} - (\frac{-2}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
10. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{2}{3} - \frac{1}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{-3}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-3}{4} - (\frac{-4}{5}) }= a^{\frac{1}{20}}\\=\sqrt[20]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{3}}}\\= y^{ \frac{5}{3} - \frac{1}{3} }= y^{\frac{4}{3}}\\=\sqrt[3]{ y^{4} }=y.\sqrt[3]{ y }\\---------------\)