Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{4}{5}}}\\= a^{ \frac{5}{3} - \frac{4}{5} }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
2. \(\dfrac{y^{\frac{1}{4}}}{y^{-1}}\\= y^{ \frac{1}{4} - (-1) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
3. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{5}) }= x^{\frac{-1}{15}}\\=\frac{1}{\sqrt[15]{ x }}=\frac{1}{\sqrt[15]{ x }}. \color{purple}{\frac{\sqrt[15]{ x^{14} }}{\sqrt[15]{ x^{14} }}} \\=\frac{\sqrt[15]{ x^{14} }}{x}\\---------------\)
4. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-3}{4} - \frac{5}{2} }= q^{\frac{-13}{4}}\\=\frac{1}{\sqrt[4]{ q^{13} }}\\=\frac{1}{|q^{3}|.\sqrt[4]{ q }}=\frac{1}{|q^{3}|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{4}|}\\---------------\)
5. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
6. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-5}{3} - \frac{5}{2} }= a^{\frac{-25}{6}}\\=\frac{1}{\sqrt[6]{ a^{25} }}\\=\frac{1}{|a^{4}|.\sqrt[6]{ a }}=\frac{1}{|a^{4}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{5}|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{5}{6} - (\frac{-1}{4}) }= y^{\frac{13}{12}}\\=\sqrt[12]{ y^{13} }=|y|.\sqrt[12]{ y }\\---------------\)
8. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{2} - (\frac{-2}{3}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-1}{5} - \frac{2}{3} }= y^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ y^{13} }}=\frac{1}{\sqrt[15]{ y^{13} }}. \color{purple}{\frac{\sqrt[15]{ y^{2} }}{\sqrt[15]{ y^{2} }}} \\=\frac{\sqrt[15]{ y^{2} }}{y}\\---------------\)
10. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{2}{3}}}\\= y^{ \frac{-4}{5} - \frac{2}{3} }= y^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ y^{22} }}\\=\frac{1}{y.\sqrt[15]{ y^{7} }}=\frac{1}{y.\sqrt[15]{ y^{7} }} \color{purple}{\frac{\sqrt[15]{ y^{8} }}{\sqrt[15]{ y^{8} }}} \\=\frac{\sqrt[15]{ y^{8} }}{y^{2}}\\---------------\)
11. \(\dfrac{q^{-1}}{q^{\frac{2}{3}}}\\= q^{ -1 - \frac{2}{3} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }} \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{6} - (\frac{-1}{3}) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)