Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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