Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-5}{4} - \frac{2}{3} }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{-3}{5}}}\\= a^{ 1 - (\frac{-3}{5}) }= a^{\frac{8}{5}}\\=\sqrt[5]{ a^{8} }=a.\sqrt[5]{ a^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{1}{4}}}\\= q^{ \frac{1}{4} - \frac{1}{4} }= q^{0}\\=1\\---------------\)
4. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{3}{4}}}\\= y^{ \frac{1}{6} - \frac{3}{4} }= y^{\frac{-7}{12}}\\=\frac{1}{\sqrt[12]{ y^{7} }}=\frac{1}{\sqrt[12]{ y^{7} }}. \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y|}\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\\= x^{ \frac{2}{3} - 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\dfrac{q^{\frac{1}{3}}}{q^{-1}}\\= q^{ \frac{1}{3} - (-1) }= q^{\frac{4}{3}}\\=\sqrt[3]{ q^{4} }=q.\sqrt[3]{ q }\\---------------\)
7. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{5}{2}}}\\= a^{ \frac{-1}{6} - \frac{5}{2} }= a^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ a^{8} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }}=\frac{1}{a^{2}.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{3}}\\---------------\)
8. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-1}{2} - (\frac{-1}{5}) }= q^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ q^{3} }}=\frac{1}{\sqrt[10]{ q^{3} }}. \color{purple}{\frac{\sqrt[10]{ q^{7} }}{\sqrt[10]{ q^{7} }}} \\=\frac{\sqrt[10]{ q^{7} }}{|q|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{1}{2} - (\frac{-1}{3}) }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{2}{5}}}\\= y^{ 1 - \frac{2}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{a^{\frac{2}{5}}}{a^{1}}\\= a^{ \frac{2}{5} - 1 }= a^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ a^{3} }}=\frac{1}{\sqrt[5]{ a^{3} }}. \color{purple}{\frac{\sqrt[5]{ a^{2} }}{\sqrt[5]{ a^{2} }}} \\=\frac{\sqrt[5]{ a^{2} }}{a}\\---------------\)