Werk uit m.b.v. de rekenregels
- \(\left(a^{\frac{5}{3}}\right)^{1}\)
- \(\left(y^{\frac{5}{6}}\right)^{\frac{-3}{4}}\)
- \(\left(y^{-1}\right)^{\frac{1}{2}}\)
- \(\left(a^{\frac{-5}{2}}\right)^{\frac{1}{3}}\)
- \(\left(q^{\frac{4}{3}}\right)^{\frac{1}{2}}\)
- \(\left(a^{\frac{4}{5}}\right)^{\frac{-5}{4}}\)
- \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{5}}\)
- \(\left(q^{\frac{2}{3}}\right)^{\frac{4}{5}}\)
- \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{3}}\)
- \(\left(x^{\frac{3}{5}}\right)^{\frac{3}{4}}\)
- \(\left(a^{-2}\right)^{\frac{5}{3}}\)
- \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{4}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(a^{\frac{5}{3}}\right)^{1}\\= a^{ \frac{5}{3} . 1 }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
- \(\left(y^{\frac{5}{6}}\right)^{\frac{-3}{4}}\\= y^{ \frac{5}{6} . (\frac{-3}{4}) }= y^{\frac{-5}{8}}\\=\frac{1}{\sqrt[8]{ y^{5} }}=\frac{1}{\sqrt[8]{ y^{5} }}.
\color{purple}{\frac{\sqrt[8]{ y^{3} }}{\sqrt[8]{ y^{3} }}} \\=\frac{\sqrt[8]{ y^{3} }}{|y|}\\---------------\)
- \(\left(y^{-1}\right)^{\frac{1}{2}}\\= y^{ -1 . \frac{1}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }.
\color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
- \(\left(a^{\frac{-5}{2}}\right)^{\frac{1}{3}}\\= a^{ \frac{-5}{2} . \frac{1}{3} }= a^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ a^{5} }}=\frac{1}{\sqrt[6]{ a^{5} }}.
\color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a|}\\---------------\)
- \(\left(q^{\frac{4}{3}}\right)^{\frac{1}{2}}\\= q^{ \frac{4}{3} . \frac{1}{2} }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
- \(\left(a^{\frac{4}{5}}\right)^{\frac{-5}{4}}\\= a^{ \frac{4}{5} . (\frac{-5}{4}) }= a^{-1}\\=\frac{1}{a}\\---------------\)
- \(\left(q^{\frac{1}{6}}\right)^{\frac{-1}{5}}\\= q^{ \frac{1}{6} . (\frac{-1}{5}) }= q^{\frac{-1}{30}}\\=\frac{1}{\sqrt[30]{ q }}=\frac{1}{\sqrt[30]{ q }}.
\color{purple}{\frac{\sqrt[30]{ q^{29} }}{\sqrt[30]{ q^{29} }}} \\=\frac{\sqrt[30]{ q^{29} }}{|q|}\\---------------\)
- \(\left(q^{\frac{2}{3}}\right)^{\frac{4}{5}}\\= q^{ \frac{2}{3} . \frac{4}{5} }= q^{\frac{8}{15}}\\=\sqrt[15]{ q^{8} }\\---------------\)
- \(\left(y^{\frac{-1}{2}}\right)^{\frac{2}{3}}\\= y^{ \frac{-1}{2} . \frac{2}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}.
\color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
- \(\left(x^{\frac{3}{5}}\right)^{\frac{3}{4}}\\= x^{ \frac{3}{5} . \frac{3}{4} }= x^{\frac{9}{20}}\\=\sqrt[20]{ x^{9} }\\---------------\)
- \(\left(a^{-2}\right)^{\frac{5}{3}}\\= a^{ -2 . \frac{5}{3} }= a^{\frac{-10}{3}}\\=\frac{1}{\sqrt[3]{ a^{10} }}\\=\frac{1}{a^{3}.\sqrt[3]{ a }}=\frac{1}{a^{3}.\sqrt[3]{ a }}
\color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{4}}\\---------------\)
- \(\left(x^{\frac{-5}{4}}\right)^{\frac{5}{4}}\\= x^{ \frac{-5}{4} . \frac{5}{4} }= x^{\frac{-25}{16}}\\=\frac{1}{\sqrt[16]{ x^{25} }}\\=\frac{1}{|x|.\sqrt[16]{ x^{9} }}=\frac{1}{|x|.\sqrt[16]{ x^{9} }}
\color{purple}{\frac{\sqrt[16]{ x^{7} }}{\sqrt[16]{ x^{7} }}} \\=\frac{\sqrt[16]{ x^{7} }}{|x^{2}|}\\---------------\)