Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{2}) }= y^{0}\\=1\\---------------\)
2. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{5}{2} - (\frac{-3}{5}) }= a^{\frac{31}{10}}\\=\sqrt[10]{ a^{31} }=|a^{3}|.\sqrt[10]{ a }\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{1}{2} - (\frac{-5}{3}) }= y^{\frac{13}{6}}\\=\sqrt[6]{ y^{13} }=|y^{2}|.\sqrt[6]{ y }\\---------------\)
4. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{1}{6}}}\\= y^{ \frac{2}{5} - \frac{1}{6} }= y^{\frac{7}{30}}\\=\sqrt[30]{ y^{7} }\\---------------\)
5. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{5}{6} - (\frac{-3}{5}) }= x^{\frac{43}{30}}\\=\sqrt[30]{ x^{43} }=|x|.\sqrt[30]{ x^{13} }\\---------------\)
6. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{3}{5} - (\frac{-1}{6}) }= y^{\frac{23}{30}}\\=\sqrt[30]{ y^{23} }\\---------------\)
8. \(\dfrac{y^{-1}}{y^{\frac{-1}{3}}}\\= y^{ -1 - (\frac{-1}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\dfrac{x^{\frac{5}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{5}{3} - (\frac{-4}{5}) }= x^{\frac{37}{15}}\\=\sqrt[15]{ x^{37} }=x^{2}.\sqrt[15]{ x^{7} }\\---------------\)
10. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{1}{3} - (\frac{-3}{4}) }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
11. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-3}{2} - \frac{1}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{-4}{5}}}{a^{1}}\\= a^{ \frac{-4}{5} - 1 }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)