Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-3}{4} - \frac{1}{2} }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
2. \(\dfrac{y^{\frac{-3}{5}}}{y^{1}}\\= y^{ \frac{-3}{5} - 1 }= y^{\frac{-8}{5}}\\=\frac{1}{\sqrt[5]{ y^{8} }}\\=\frac{1}{y.\sqrt[5]{ y^{3} }}=\frac{1}{y.\sqrt[5]{ y^{3} }} \color{purple}{\frac{\sqrt[5]{ y^{2} }}{\sqrt[5]{ y^{2} }}} \\=\frac{\sqrt[5]{ y^{2} }}{y^{2}}\\---------------\)
3. \(\dfrac{x^{-1}}{x^{\frac{-2}{5}}}\\= x^{ -1 - (\frac{-2}{5}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{3}{5}}}\\= q^{ 1 - \frac{3}{5} }= q^{\frac{2}{5}}\\=\sqrt[5]{ q^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{1}{2}}}{y^{2}}\\= y^{ \frac{1}{2} - 2 }= y^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ y^{3} } }\\=\frac{1}{|y|. \sqrt{ y } }=\frac{1}{|y|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{2}|}\\---------------\)
6. \(\dfrac{a^{\frac{-2}{3}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-2}{3} - \frac{5}{4} }= a^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ a^{23} }}\\=\frac{1}{|a|.\sqrt[12]{ a^{11} }}=\frac{1}{|a|.\sqrt[12]{ a^{11} }} \color{purple}{\frac{\sqrt[12]{ a }}{\sqrt[12]{ a }}} \\=\frac{\sqrt[12]{ a }}{|a^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{5}{3} - (\frac{-5}{6}) }= y^{\frac{5}{2}}\\= \sqrt{ y^{5} } =|y^{2}|. \sqrt{ y } \\---------------\)
8. \(\dfrac{a^{\frac{5}{2}}}{a^{2}}\\= a^{ \frac{5}{2} - 2 }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
9. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-5}{6} - \frac{3}{5} }= y^{\frac{-43}{30}}\\=\frac{1}{\sqrt[30]{ y^{43} }}\\=\frac{1}{|y|.\sqrt[30]{ y^{13} }}=\frac{1}{|y|.\sqrt[30]{ y^{13} }} \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y^{2}|}\\---------------\)
10. \(\dfrac{q^{\frac{-3}{4}}}{q^{1}}\\= q^{ \frac{-3}{4} - 1 }= q^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[4]{ q^{3} }}=\frac{1}{|q|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-2}{3}}}\\= y^{ \frac{-3}{5} - (\frac{-2}{3}) }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
12. \(\dfrac{a^{\frac{4}{3}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{4}{3} - (\frac{-1}{6}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)