Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{-1}{5} - \frac{3}{4} }= x^{\frac{-19}{20}}\\=\frac{1}{\sqrt[20]{ x^{19} }}=\frac{1}{\sqrt[20]{ x^{19} }}. \color{purple}{\frac{\sqrt[20]{ x }}{\sqrt[20]{ x }}} \\=\frac{\sqrt[20]{ x }}{|x|}\\---------------\)
2. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{2}) }= y^{2}\\\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{2}) }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
4. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{3}{2} - (\frac{-2}{3}) }= a^{\frac{13}{6}}\\=\sqrt[6]{ a^{13} }=|a^{2}|.\sqrt[6]{ a }\\---------------\)
5. \(\dfrac{a^{\frac{-2}{3}}}{a^{1}}\\= a^{ \frac{-2}{3} - 1 }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
6. \(\dfrac{a^{-1}}{a^{\frac{-1}{3}}}\\= a^{ -1 - (\frac{-1}{3}) }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
7. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-4}{3} - \frac{3}{4} }= a^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ a^{25} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a }}=\frac{1}{|a^{2}|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{3}|}\\---------------\)
8. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{1}{4} - (\frac{-1}{4}) }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
9. \(\dfrac{a^{1}}{a^{\frac{-1}{2}}}\\= a^{ 1 - (\frac{-1}{2}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{-3}{5}}}\\= y^{ 1 - (\frac{-3}{5}) }= y^{\frac{8}{5}}\\=\sqrt[5]{ y^{8} }=y.\sqrt[5]{ y^{3} }\\---------------\)
11. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-1}{5} - (\frac{-1}{4}) }= y^{\frac{1}{20}}\\=\sqrt[20]{ y }\\---------------\)
12. \(\dfrac{q^{\frac{4}{5}}}{q^{1}}\\= q^{ \frac{4}{5} - 1 }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)