Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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