Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{5}{2}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{5}{2} - (\frac{-3}{2}) }= x^{4}\\\\---------------\)
2. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{4}{5}}}\\= x^{ \frac{-1}{3} - \frac{4}{5} }= x^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ x^{17} }}\\=\frac{1}{x.\sqrt[15]{ x^{2} }}=\frac{1}{x.\sqrt[15]{ x^{2} }} \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x^{2}}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{3}}}{y^{1}}\\= y^{ \frac{-5}{3} - 1 }= y^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ y^{8} }}\\=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }}=\frac{1}{y^{2}.\sqrt[3]{ y^{2} }} \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y^{3}}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{-1}{4}}}{y^{1}}\\= y^{ \frac{-1}{4} - 1 }= y^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ y^{5} }}\\=\frac{1}{|y|.\sqrt[4]{ y }}=\frac{1}{|y|.\sqrt[4]{ y }} \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y^{2}|}\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{1}{6}}}\\= a^{ 1 - \frac{1}{6} }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
7. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{3}{2} - (\frac{-1}{4}) }= y^{\frac{7}{4}}\\=\sqrt[4]{ y^{7} }=|y|.\sqrt[4]{ y^{3} }\\---------------\)
8. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{3} - \frac{1}{2} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)
9. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-2}{5}}}\\= x^{ \frac{1}{4} - (\frac{-2}{5}) }= x^{\frac{13}{20}}\\=\sqrt[20]{ x^{13} }\\---------------\)
10. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-1}{6} - (\frac{-1}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
11. \(\dfrac{q^{\frac{3}{4}}}{q^{-1}}\\= q^{ \frac{3}{4} - (-1) }= q^{\frac{7}{4}}\\=\sqrt[4]{ q^{7} }=|q|.\sqrt[4]{ q^{3} }\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-4}{3} - (\frac{-5}{4}) }= a^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ a }}=\frac{1}{\sqrt[12]{ a }}. \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a|}\\---------------\)