Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-5}{2} - \frac{5}{2} }= q^{-5}\\=\frac{1}{q^{5}}\\---------------\)
2. \(\dfrac{q^{\frac{5}{4}}}{q^{-2}}\\= q^{ \frac{5}{4} - (-2) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)
3. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-3}{4} - \frac{3}{5} }= y^{\frac{-27}{20}}\\=\frac{1}{\sqrt[20]{ y^{27} }}\\=\frac{1}{|y|.\sqrt[20]{ y^{7} }}=\frac{1}{|y|.\sqrt[20]{ y^{7} }} \color{purple}{\frac{\sqrt[20]{ y^{13} }}{\sqrt[20]{ y^{13} }}} \\=\frac{\sqrt[20]{ y^{13} }}{|y^{2}|}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{3} - \frac{5}{6} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
5. \(\dfrac{y^{1}}{y^{-2}}\\= y^{ 1 - (-2) }= y^{3}\\\\---------------\)
6. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{3} - (\frac{-1}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
7. \(\dfrac{x^{\frac{1}{3}}}{x^{2}}\\= x^{ \frac{1}{3} - 2 }= x^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ x^{5} }}\\=\frac{1}{x.\sqrt[3]{ x^{2} }}=\frac{1}{x.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{2}}\\---------------\)
8. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-1}{4}}}\\= x^{ \frac{5}{3} - (\frac{-1}{4}) }= x^{\frac{23}{12}}\\=\sqrt[12]{ x^{23} }=|x|.\sqrt[12]{ x^{11} }\\---------------\)
9. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{5}{4} - (\frac{-1}{2}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{5}{2} - (\frac{-5}{2}) }= y^{5}\\\\---------------\)
11. \(\dfrac{y^{\frac{-3}{4}}}{y^{-1}}\\= y^{ \frac{-3}{4} - (-1) }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
12. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{3}}}\\= y^{ \frac{3}{4} - \frac{1}{3} }= y^{\frac{5}{12}}\\=\sqrt[12]{ y^{5} }\\---------------\)