Question

Simplify:

(1) ${\left(18\right)}^{\frac{1}{3}}\times {\left(18\right)}^{\frac{1}{2}}$
(2) $x^{\frac{2}{3}}\times x^{\frac{1}{3}}$
(3) ${\left(y^{\frac{2}{3}}\right)}^{\frac{3}{4}}$
(4) $m^{\frac{14}{5}}÷m^{\frac{4}{5}}$

Answer 1

(1) ${\left(18\right)}^{\frac{1}{3}}\times {\left(18\right)}^{\frac{1}{2}}$ can be written as ${\left(18\right)}^{\frac{1}{3}+\frac{1}{2}}={\left(18\right)}^{\frac{5}{6}}$
(2) $x^{\frac{2}{3}}\times x^{\frac{1}{3}}$ can be written as ${\left(x\right)}^{\frac{2}{3}+\frac{1}{3}}={\left(x\right)}^{\frac{3}{3}}=x$
(3) ${\left(y^{\frac{2}{3}}\right)}^{\frac{3}{4}}$ can be written as ${\left(y\right)}^{\frac{2}{3}\times \frac{3}{4}}={\left(y\right)}^{\frac{1}{2}}$
(4) $m^{\frac{14}{5}}÷m^{\frac{4}{5}}$can be written as $m^{\frac{14}{5}-\frac{4}{5}}=m^{\frac{10}{5}}=m^2$