Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-2}{5}}}{y^{1}}\\= y^{ \frac{-2}{5} - 1 }= y^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ y^{7} }}\\=\frac{1}{y.\sqrt[5]{ y^{2} }}=\frac{1}{y.\sqrt[5]{ y^{2} }} \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y^{2}}\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-3}{5}}}\\= y^{ -1 - (\frac{-3}{5}) }= y^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ y^{2} }}=\frac{1}{\sqrt[5]{ y^{2} }}. \color{purple}{\frac{\sqrt[5]{ y^{3} }}{\sqrt[5]{ y^{3} }}} \\=\frac{\sqrt[5]{ y^{3} }}{y}\\---------------\)
3. \(\dfrac{a^{1}}{a^{\frac{-2}{3}}}\\= a^{ 1 - (\frac{-2}{3}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
4. \(\dfrac{x^{\frac{3}{2}}}{x^{1}}\\= x^{ \frac{3}{2} - 1 }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{2}{3} - (\frac{-5}{3}) }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{1}{5}}}\\= q^{ \frac{3}{2} - \frac{1}{5} }= q^{\frac{13}{10}}\\=\sqrt[10]{ q^{13} }=|q|.\sqrt[10]{ q^{3} }\\---------------\)
7. \(\dfrac{q^{\frac{5}{2}}}{q^{-2}}\\= q^{ \frac{5}{2} - (-2) }= q^{\frac{9}{2}}\\= \sqrt{ q^{9} } =|q^{4}|. \sqrt{ q } \\---------------\)
8. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{3}{4} - (\frac{-2}{5}) }= q^{\frac{23}{20}}\\=\sqrt[20]{ q^{23} }=|q|.\sqrt[20]{ q^{3} }\\---------------\)
9. \(\dfrac{q^{-2}}{q^{\frac{1}{2}}}\\= q^{ -2 - \frac{1}{2} }= q^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ q^{5} } }\\=\frac{1}{|q^{2}|. \sqrt{ q } }=\frac{1}{|q^{2}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{3}|}\\---------------\)
10. \(\dfrac{a^{-1}}{a^{-2}}\\= a^{ -1 - (-2) }= a^{1}\\\\---------------\)
11. \(\dfrac{q^{\frac{-5}{3}}}{q^{1}}\\= q^{ \frac{-5}{3} - 1 }= q^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ q^{8} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }}=\frac{1}{q^{2}.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{3}}\\---------------\)
12. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{-5}{4} - (\frac{-1}{5}) }= a^{\frac{-21}{20}}\\=\frac{1}{\sqrt[20]{ a^{21} }}\\=\frac{1}{|a|.\sqrt[20]{ a }}=\frac{1}{|a|.\sqrt[20]{ a }} \color{purple}{\frac{\sqrt[20]{ a^{19} }}{\sqrt[20]{ a^{19} }}} \\=\frac{\sqrt[20]{ a^{19} }}{|a^{2}|}\\---------------\)