Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{-1}}\\= y^{ \frac{-1}{2} - (-1) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
2. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{5}{4}}}\\= q^{ \frac{1}{6} - \frac{5}{4} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{2} - (\frac{-2}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{2}}}\\= x^{ \frac{-1}{2} - \frac{1}{2} }= x^{-1}\\=\frac{1}{x}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{4} - (\frac{-1}{3}) }= y^{\frac{1}{12}}\\=\sqrt[12]{ y }\\---------------\)
6. \(\dfrac{x^{-1}}{x^{\frac{1}{2}}}\\= x^{ -1 - \frac{1}{2} }= x^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ x^{3} } }\\=\frac{1}{|x|. \sqrt{ x } }=\frac{1}{|x|. \sqrt{ x } } \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x^{2}|}\\---------------\)
7. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{5} - (\frac{-2}{3}) }= q^{\frac{7}{15}}\\=\sqrt[15]{ q^{7} }\\---------------\)
8. \(\dfrac{a^{\frac{-1}{5}}}{a^{\frac{5}{4}}}\\= a^{ \frac{-1}{5} - \frac{5}{4} }= a^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ a^{29} }}\\=\frac{1}{|a|.\sqrt[20]{ a^{9} }}=\frac{1}{|a|.\sqrt[20]{ a^{9} }} \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{-5}{2}}}\\= q^{ \frac{5}{6} - (\frac{-5}{2}) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{3}{5} - (\frac{-1}{5}) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
11. \(\dfrac{q^{\frac{3}{5}}}{q^{-1}}\\= q^{ \frac{3}{5} - (-1) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-5}{4} - \frac{3}{4} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)