# How do you simplify (5k^2m)^3[(4km^4)^2]^2?

Oct 22, 2017

$\implies 32000 {k}^{10} {m}^{19}$

#### Explanation:

${\left(5 {k}^{2} m\right)}^{3} {\left[{\left(4 k {m}^{4}\right)}^{2}\right]}^{2}$

Use Rule: ${\left({a}^{m}\right)}^{n} = {a}^{m n}$

(5^3k^(2xx3)m^3[(4^2k^2m^(4xx2)]^2

$\implies \left(125 {k}^{6} {m}^{3}\right) {\left[\left(16 {k}^{2} {m}^{8}\right)\right]}^{2}$

=>(125k^6m^3)(16^2k^(2xx2)m^(8xx2)

$\implies \left(125 {k}^{6} {m}^{3}\right) \left(256 {k}^{4} {m}^{16}\right)$

Use Rule : ${a}^{m} \setminus \times {a}^{n} = {a}^{m + n}$

$\implies 125 \times 256 {k}^{6 + 4} {m}^{3 + 16}$

$\implies 32000 {k}^{10} {m}^{19}$

this can be written as :

$\implies {2}^{5} \times {10}^{3} {k}^{10} {m}^{19}$ -----------as $32000 = {2}^{5} \times {10}^{3}$