Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{1}}{y^{\frac{5}{6}}}\\= y^{ 1 - \frac{5}{6} }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{2}{5} - (\frac{-1}{5}) }= x^{\frac{3}{5}}\\=\sqrt[5]{ x^{3} }\\---------------\)
3. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-4}{3} - (\frac{-1}{3}) }= y^{-1}\\=\frac{1}{y}\\---------------\)
4. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{2}) }= q^{0}\\=1\\---------------\)
5. \(\dfrac{a^{\frac{5}{3}}}{a^{-1}}\\= a^{ \frac{5}{3} - (-1) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
6. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-3}{5}) }= x^{\frac{4}{15}}\\=\sqrt[15]{ x^{4} }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{5} - (\frac{-1}{3}) }= a^{\frac{2}{15}}\\=\sqrt[15]{ a^{2} }\\---------------\)
8. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{3}) }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{2} - \frac{4}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
10. \(\dfrac{q^{\frac{5}{2}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{5}{2} - (\frac{-2}{5}) }= q^{\frac{29}{10}}\\=\sqrt[10]{ q^{29} }=|q^{2}|.\sqrt[10]{ q^{9} }\\---------------\)
11. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-4}{5} - \frac{4}{5} }= x^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ x^{8} }}\\=\frac{1}{x.\sqrt[5]{ x^{3} }}=\frac{1}{x.\sqrt[5]{ x^{3} }} \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x^{2}}\\---------------\)
12. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{3}{5} - (\frac{-5}{4}) }= x^{\frac{37}{20}}\\=\sqrt[20]{ x^{37} }=|x|.\sqrt[20]{ x^{17} }\\---------------\)