Werk uit m.b.v. de rekenregels
- \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{3}}}\)
- \(\dfrac{q^{\frac{4}{3}}}{q^{2}}\)
- \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\)
- \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{1}{3}}}\)
- \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{5}}}\)
- \(\dfrac{x^{\frac{5}{2}}}{x^{1}}\)
- \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\)
- \(\dfrac{y^{-1}}{y^{\frac{1}{3}}}\)
- \(\dfrac{x^{1}}{x^{\frac{-1}{6}}}\)
- \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{2}}}\)
- \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{2}}}\)
- \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{1}{3}}}\\= q^{ \frac{1}{3} - \frac{1}{3} }= q^{0}\\=1\\---------------\)
- \(\dfrac{q^{\frac{4}{3}}}{q^{2}}\\= q^{ \frac{4}{3} - 2 }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}.
\color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
- \(\dfrac{a^{\frac{-4}{3}}}{a^{1}}\\= a^{ \frac{-4}{3} - 1 }= a^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ a^{7} }}\\=\frac{1}{a^{2}.\sqrt[3]{ a }}=\frac{1}{a^{2}.\sqrt[3]{ a }}
\color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{3}}\\---------------\)
- \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{1}{3}}}\\= q^{ \frac{3}{2} - \frac{1}{3} }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
- \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{2}{3} - (\frac{-1}{5}) }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
- \(\dfrac{x^{\frac{5}{2}}}{x^{1}}\\= x^{ \frac{5}{2} - 1 }= x^{\frac{3}{2}}\\= \sqrt{ x^{3} } =|x|. \sqrt{ x } \\---------------\)
- \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
- \(\dfrac{y^{-1}}{y^{\frac{1}{3}}}\\= y^{ -1 - \frac{1}{3} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }}
\color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
- \(\dfrac{x^{1}}{x^{\frac{-1}{6}}}\\= x^{ 1 - (\frac{-1}{6}) }= x^{\frac{7}{6}}\\=\sqrt[6]{ x^{7} }=|x|.\sqrt[6]{ x }\\---------------\)
- \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-2}{3} - (\frac{-3}{2}) }= x^{\frac{5}{6}}\\=\sqrt[6]{ x^{5} }\\---------------\)
- \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{5}{2}}}\\= q^{ \frac{5}{6} - \frac{5}{2} }= q^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ q^{5} }}\\=\frac{1}{q.\sqrt[3]{ q^{2} }}=\frac{1}{q.\sqrt[3]{ q^{2} }}
\color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q^{2}}\\---------------\)
- \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{2}) }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)