Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{5}{3}}}\\= a^{ \frac{-4}{5} - \frac{5}{3} }= a^{\frac{-37}{15}}\\=\frac{1}{\sqrt[15]{ a^{37} }}\\=\frac{1}{a^{2}.\sqrt[15]{ a^{7} }}=\frac{1}{a^{2}.\sqrt[15]{ a^{7} }} \color{purple}{\frac{\sqrt[15]{ a^{8} }}{\sqrt[15]{ a^{8} }}} \\=\frac{\sqrt[15]{ a^{8} }}{a^{3}}\\---------------\)
2. \(\dfrac{y^{\frac{-5}{4}}}{y^{-1}}\\= y^{ \frac{-5}{4} - (-1) }= y^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ y }}=\frac{1}{\sqrt[4]{ y }}. \color{purple}{\frac{\sqrt[4]{ y^{3} }}{\sqrt[4]{ y^{3} }}} \\=\frac{\sqrt[4]{ y^{3} }}{|y|}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-5}{2} - \frac{4}{3} }= y^{\frac{-23}{6}}\\=\frac{1}{\sqrt[6]{ y^{23} }}\\=\frac{1}{|y^{3}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{3}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{4}|}\\---------------\)
4. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{5}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
5. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{4}) }= y^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ y^{5} }}=\frac{1}{\sqrt[12]{ y^{5} }}. \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y|}\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{4}{3}}}\\= x^{ \frac{2}{3} - \frac{4}{3} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
7. \(\dfrac{a^{\frac{3}{2}}}{a^{\frac{3}{5}}}\\= a^{ \frac{3}{2} - \frac{3}{5} }= a^{\frac{9}{10}}\\=\sqrt[10]{ a^{9} }\\---------------\)
8. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{-4}{3} - \frac{2}{5} }= a^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ a^{26} }}\\=\frac{1}{a.\sqrt[15]{ a^{11} }}=\frac{1}{a.\sqrt[15]{ a^{11} }} \color{purple}{\frac{\sqrt[15]{ a^{4} }}{\sqrt[15]{ a^{4} }}} \\=\frac{\sqrt[15]{ a^{4} }}{a^{2}}\\---------------\)
9. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{3} - \frac{4}{3} }= q^{-1}\\=\frac{1}{q}\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{2} - \frac{1}{4} }= y^{\frac{1}{4}}\\=\sqrt[4]{ y }\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\dfrac{q^{\frac{5}{4}}}{q^{-2}}\\= q^{ \frac{5}{4} - (-2) }= q^{\frac{13}{4}}\\=\sqrt[4]{ q^{13} }=|q^{3}|.\sqrt[4]{ q }\\---------------\)