# How do you simplify (-2g^3h)(-3gj^4)^2(-ghj^4)^2?

Jan 24, 2017

$= - 18 {g}^{7} {h}^{3} {j}^{16}$

#### Explanation:

Simplify each bracket separately, then multiply all the factors together:

$\textcolor{red}{\left(- 2 {g}^{3} h\right)} \textcolor{b l u e}{{\left(- 3 g {j}^{4}\right)}^{2}} \textcolor{b r o w n}{{\left(- g h {j}^{4}\right)}^{2}}$

=color(red)((-2g^3h))color(blue)((+9g^2j^8)color(brown)((+g^2h^2j^8)

$= - 18 \times {g}^{3} {g}^{2} {g}^{2} \times h {h}^{2} \times {j}^{8} {j}^{8}$

$= - 18 {g}^{7} {h}^{3} {j}^{16}$

Laws of indices:

${\left({x}^{m}\right)}^{n} = {x}^{m n}$

and

${x}^{m} \times {x}^{n} = {x}^{m + n}$