# How do you simplify  ( - 9m ^ { \frac { 1} { 2} } n ^ { \frac { 4} { 5} } ) ( 2m ^ { \frac { 1} { 3} } n ^ { \frac { 2} { 5} } ) ?

$\left(- 9 {m}^{\frac{1}{2}} {n}^{\frac{4}{5}}\right) \left(2 {m}^{\frac{1}{3}} {n}^{\frac{2}{5}}\right) = - 18 {m}^{\frac{5}{6}} {n}^{\frac{6}{5}}$

#### Explanation:

$\left(- 9 {m}^{\frac{1}{2}} {n}^{\frac{4}{5}}\right) \left(2 {m}^{\frac{1}{3}} {n}^{\frac{2}{5}}\right) = - 9 \times 2 \times {m}^{\frac{1}{2}} {m}^{\frac{1}{3}} {n}^{\frac{4}{5}} {n}^{\frac{2}{5}}$
$- 9 \times 2 = - 18$
${m}^{\frac{1}{3}} {n}^{\frac{4}{5}} = {m}^{\frac{1}{2} + \frac{1}{3}} = {m}^{\frac{3 + 2}{2 \times 3}} = {m}^{\frac{5}{6}}$
${n}^{\frac{4}{5}} {n}^{\frac{2}{5}} = {n}^{\frac{4}{5} + \frac{2}{5}} = {n}^{\frac{4 + 2}{5}} = {n}^{\frac{6}{5}}$

Thus,
$9 \times 2 \times {m}^{\frac{1}{2}} {m}^{\frac{1}{3}} {n}^{\frac{4}{5}} {n}^{\frac{2}{5}} = - 18 {m}^{\frac{5}{6}} {n}^{\frac{6}{5}}$
Now,

$\left(- 9 {m}^{\frac{1}{2}} {n}^{\frac{4}{5}}\right) \left(2 {m}^{\frac{1}{3}} {n}^{\frac{2}{5}}\right) = - 18 {m}^{\frac{5}{6}} {n}^{\frac{6}{5}}$

Mar 3, 2018

-18${m}^{\frac{5}{6}}$${n}^{\frac{6}{5}}$

#### Explanation:

• Multiply the like terms (constant with constant, m with m and n with n)
• Multiplying like terms means the addition of their powers. So ${m}^{\frac{1}{2}} \cdot {m}^{\frac{1}{3}}$ = ${m}^{\left(\frac{1}{2}\right) + \left(\frac{1}{3}\right)}$ and ${n}^{\frac{4}{5}} \cdot {n}^{\frac{2}{5}}$ = ${n}^{\left(\frac{4}{5}\right) + \left(\frac{2}{5}\right)}$
• Also multiply the constants -9 and 2 to get the answer
Mar 3, 2018

$- 18 {m}^{\frac{5}{6}} {n}^{\frac{6}{5}}$

#### Explanation:

$\left(- 9 {m}^{\frac{1}{2}} {n}^{\frac{4}{5}}\right) \left(2 {m}^{\frac{1}{3}} {n}^{\frac{2}{5}}\right)$

$\therefore = - 18 {m}^{\frac{1}{2} + \frac{1}{3}} {n}^{\frac{4}{5} + \frac{2}{5}}$

$\therefore = - 18 {m}^{\frac{3 + 2}{6}} {n}^{\frac{6}{5}}$

$\therefore = - 18 {m}^{\frac{5}{6}} {n}^{\frac{6}{5}}$