Werk uit m.b.v. de rekenregels
- \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{3}}\)
- \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{4}}\)
- \(\left(q^{\frac{3}{4}}\right)^{\frac{-5}{2}}\)
- \(\left(q^{-2}\right)^{-2}\)
- \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{3}}\)
- \(\left(y^{\frac{-2}{5}}\right)^{\frac{-5}{4}}\)
- \(\left(q^{1}\right)^{\frac{1}{2}}\)
- \(\left(q^{\frac{3}{4}}\right)^{\frac{-4}{3}}\)
- \(\left(x^{-1}\right)^{\frac{1}{2}}\)
- \(\left(q^{\frac{3}{5}}\right)^{-1}\)
- \(\left(q^{-1}\right)^{\frac{3}{2}}\)
- \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{2}}\)
Werk uit m.b.v. de rekenregels
Verbetersleutel
- \(\left(q^{\frac{3}{5}}\right)^{\frac{-1}{3}}\\= q^{ \frac{3}{5} . (\frac{-1}{3}) }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}.
\color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
- \(\left(y^{\frac{5}{6}}\right)^{\frac{-5}{4}}\\= y^{ \frac{5}{6} . (\frac{-5}{4}) }= y^{\frac{-25}{24}}\\=\frac{1}{\sqrt[24]{ y^{25} }}\\=\frac{1}{|y|.\sqrt[24]{ y }}=\frac{1}{|y|.\sqrt[24]{ y }}
\color{purple}{\frac{\sqrt[24]{ y^{23} }}{\sqrt[24]{ y^{23} }}} \\=\frac{\sqrt[24]{ y^{23} }}{|y^{2}|}\\---------------\)
- \(\left(q^{\frac{3}{4}}\right)^{\frac{-5}{2}}\\= q^{ \frac{3}{4} . (\frac{-5}{2}) }= q^{\frac{-15}{8}}\\=\frac{1}{\sqrt[8]{ q^{15} }}\\=\frac{1}{|q|.\sqrt[8]{ q^{7} }}=\frac{1}{|q|.\sqrt[8]{ q^{7} }}
\color{purple}{\frac{\sqrt[8]{ q }}{\sqrt[8]{ q }}} \\=\frac{\sqrt[8]{ q }}{|q^{2}|}\\---------------\)
- \(\left(q^{-2}\right)^{-2}\\= q^{ -2 . (-2) }= q^{4}\\\\---------------\)
- \(\left(y^{\frac{1}{2}}\right)^{\frac{-4}{3}}\\= y^{ \frac{1}{2} . (\frac{-4}{3}) }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}.
\color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
- \(\left(y^{\frac{-2}{5}}\right)^{\frac{-5}{4}}\\= y^{ \frac{-2}{5} . (\frac{-5}{4}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
- \(\left(q^{1}\right)^{\frac{1}{2}}\\= q^{ 1 . \frac{1}{2} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
- \(\left(q^{\frac{3}{4}}\right)^{\frac{-4}{3}}\\= q^{ \frac{3}{4} . (\frac{-4}{3}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
- \(\left(x^{-1}\right)^{\frac{1}{2}}\\= x^{ -1 . \frac{1}{2} }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }.
\color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
- \(\left(q^{\frac{3}{5}}\right)^{-1}\\= q^{ \frac{3}{5} . (-1) }= q^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ q^{3} }}=\frac{1}{\sqrt[5]{ q^{3} }}.
\color{purple}{\frac{\sqrt[5]{ q^{2} }}{\sqrt[5]{ q^{2} }}} \\=\frac{\sqrt[5]{ q^{2} }}{q}\\---------------\)
- \(\left(q^{-1}\right)^{\frac{3}{2}}\\= q^{ -1 . \frac{3}{2} }= q^{\frac{-3}{2}}\\=\frac{1}{ \sqrt{ q^{3} } }\\=\frac{1}{|q|. \sqrt{ q } }=\frac{1}{|q|. \sqrt{ q } }
\color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{2}|}\\---------------\)
- \(\left(a^{\frac{-5}{6}}\right)^{\frac{1}{2}}\\= a^{ \frac{-5}{6} . \frac{1}{2} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}.
\color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)