Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{3}{4}}}\\= y^{ \frac{5}{6} - \frac{3}{4} }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
2. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{3}{4} - (\frac{-3}{4}) }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
3. \(\dfrac{a^{-1}}{a^{2}}\\= a^{ -1 - 2 }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
4. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{3} - \frac{1}{5} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
5. \(\dfrac{y^{-2}}{y^{\frac{-2}{5}}}\\= y^{ -2 - (\frac{-2}{5}) }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
6. \(\dfrac{y^{\frac{-2}{5}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-2}{5} - (\frac{-3}{4}) }= y^{\frac{7}{20}}\\=\sqrt[20]{ y^{7} }\\---------------\)
7. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{2}{5} - (\frac{-4}{5}) }= a^{\frac{6}{5}}\\=\sqrt[5]{ a^{6} }=a.\sqrt[5]{ a }\\---------------\)
8. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{3} - (\frac{-1}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
9. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{3} - (\frac{-1}{3}) }= a^{0}\\=1\\---------------\)
10. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-5}{4} - (\frac{-3}{4}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
11. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{5}) }= a^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ a^{21} }}\\=\frac{1}{|a|.\sqrt[20]{ a }}=\frac{1}{|a|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{x^{\frac{-5}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-5}{3} - (\frac{-1}{3}) }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)