How do you combine like terms in 3x ^ { 4} y ^ { 9} \cdot 9x ^ { 5}?

May 7, 2018

$\implies {\left(3 {x}^{3} {y}^{3}\right)}^{3}$

Explanation:

If terms are multiplied, then the powers are added.
If terms are divided, then the powers are subtracted.

$3 {x}^{4} {y}^{9} \cdot 9 {x}^{5}$

$= \left(3\right) \left(9\right) {x}^{4 + 5} {y}^{9}$

$= 27 {x}^{9} {y}^{9}$

This can actually be simplified further by pulling out a common power of $3$

$= {3}^{3} {\left({x}^{3}\right)}^{3} {\left({y}^{3}\right)}^{3}$

$= {\left(3 {x}^{3} {y}^{3}\right)}^{3}$