Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-2}{5} - (\frac{-2}{5}) }= q^{0}\\=1\\---------------\)
2. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-5}{2} - (\frac{-1}{3}) }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
3. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-2}{3}) }= x^{\frac{1}{15}}\\=\sqrt[15]{ x }\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{-1}}\\= y^{ \frac{-5}{4} - (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
5. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-4}{3} - \frac{3}{4} }= a^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ a^{25} }}\\=\frac{1}{|a^{2}|.\sqrt[12]{ a }}=\frac{1}{|a^{2}|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{3}|}\\---------------\)
6. \(\dfrac{a^{1}}{a^{\frac{-1}{3}}}\\= a^{ 1 - (\frac{-1}{3}) }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
7. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{1}{3}}}\\= y^{ \frac{3}{2} - \frac{1}{3} }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)
8. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{2}{3} - (\frac{-1}{3}) }= y^{1}\\\\---------------\)
9. \(\dfrac{a^{-1}}{a^{\frac{4}{3}}}\\= a^{ -1 - \frac{4}{3} }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
10. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}\\= y^{ \frac{3}{4} - \frac{1}{2} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{q^{\frac{-5}{6}}}{q^{1}}\\= q^{ \frac{-5}{6} - 1 }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
12. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{2}{3} - \frac{5}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)