Mathematics, 23.07.2019 10:30 tabathahasaunicorn1
What does (-54x^6/y^4)^2/3 equal to?
Answers: 1
![\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------](/tpl/images/0123/0838/17c78.png)
![\bf \left( \cfrac{-54x^6}{y^4} \right)^{\frac{2}{3}}\impliedby \textit{and now let's distribute the exponent} \\\\\\ \left( \cfrac{(-54)^{\frac{2}{3}}x^{6\cdot \frac{2}{3}}}{y^{4\cdot \frac{2}{3}}} \right)\implies \cfrac{(-54)^{\frac{2}{3}}x^4}{y^{\frac{8}{3}}}\implies \cfrac{\sqrt[3]{(-54)^2}~x^4}{\sqrt[3]{y^8}}\implies \cfrac{\sqrt[3]{2916}~x^4}{\sqrt[3]{y^6y^2}} \\\\\\ \cfrac{\sqrt[3]{4\cdot 9^3}~x^4}{\sqrt[3]{(y^2)^3y^2}}\implies \cfrac{9\sqrt[3]{4}~x^4}{y^2\sqrt[3]{y^2}}](/tpl/images/0123/0838/59c4a.png)
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