Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{4}}}{q^{-1}}\\= q^{ \frac{5}{4} - (-1) }= q^{\frac{9}{4}}\\=\sqrt[4]{ q^{9} }=|q^{2}|.\sqrt[4]{ q }\\---------------\)
2. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{-1}{2} - (\frac{-5}{3}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
4. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{3} - \frac{2}{3} }= y^{-1}\\=\frac{1}{y}\\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{2} - (\frac{-1}{2}) }= x^{2}\\\\---------------\)
6. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{6} - (\frac{-3}{5}) }= y^{\frac{23}{30}}\\=\sqrt[30]{ y^{23} }\\---------------\)
8. \(\dfrac{q^{-1}}{q^{\frac{-5}{4}}}\\= q^{ -1 - (\frac{-5}{4}) }= q^{\frac{1}{4}}\\=\sqrt[4]{ q }\\---------------\)
9. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{4}{3} - (\frac{-5}{6}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
10. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-1}{3} - \frac{5}{3} }= q^{-2}\\=\frac{1}{q^{2}}\\---------------\)
11. \(\dfrac{a^{\frac{1}{2}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{2} - \frac{1}{2} }= a^{0}\\=1\\---------------\)
12. \(\dfrac{q^{\frac{-1}{5}}}{q^{1}}\\= q^{ \frac{-1}{5} - 1 }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)