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

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Answer 1 · 2017-10-22T01:45:51

$\Rightarrow 32000 k^{10} m^{19}$ $=> 32000 k^10 m^19$

${(5 k^{2} m)}^{3} {[{(4 k m^{4})}^{2}]}^{2}$ $(5k^2m)^3[(4km^4)^2]^2$

Use Rule: ${(a^{m})}^{n} = a^{m n}$ $(a^m)^n = a^(mn)$

$(5^{3} k^{2 \times 3} m^{3} [{(4^{2} k^{2} m^{4 \times 2}]}^{2}$ $(5^3k^(2xx3)m^3[(4^2k^2m^(4xx2)]^2$

$\Rightarrow (125 k^{6} m^{3}) {[(16 k^{2} m^{8})]}^{2}$ $=>(125k^6m^3)[(16k^2m^8)]^2$

$\Rightarrow (125 k^{6} m^{3}) (16^{2} k^{2 \times 2} m^{8 \times 2}$ $=>(125k^6m^3)(16^2k^(2xx2)m^(8xx2)$

$\Rightarrow (125 k^{6} m^{3}) (256 k^{4} m^{16})$ $=>(125k^6m^3)(256k^4m^16)$

Use Rule : $a^m\ times a^n = a^(m+n)$

$=> 125xx256 k^(6+4) m^(3+16)$

$=> 32000 k^10 m^19$

this can be written as :

$=> 2^5xx10^3k^10m^19$ -----------as $32000= 2^5 xx 10^3$

How do you simplify (5k^2m)^3[(4km^4)^2]^2(5k2m)3[(4km4)2]2(5k^2m)^3[(4km^4)^2]^2?