Question

How yo simplify (b2/3 x b5/3 x t1/5 x t3/4)?

Answer 1

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------$

$\bf b^{\frac{2}{3}}\cdot b^{\frac{5}{3}}\cdot t^{\frac{1}{5}}\cdot t^{\frac{3}{5}}\implies b^{\frac{2}{3}+\frac{5}{3}}\cdot t^{\frac{1}{5}+\frac{3}{5}}\implies b^{\frac{7}{3}}t^{\frac{4}{5}}\implies \sqrt[3]{b^7}\cdot \sqrt[5]{t^4} \\\\\\ \sqrt[3]{b^{1+3+3}}\cdot \sqrt[5]{t^4}\implies \sqrt[3]{b^1b^3b^3}\cdot \sqrt[5]{t^4}\implies bb\sqrt[3]{b}\cdot \sqrt[5]{t^4}\implies b^2\sqrt[3]{b}\cdot \sqrt[5]{t^4}$