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

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Answer 1 · 2017-10-22T01:45:51

# => 32000 k^10 m^19#

#(5k^2m)^3[(4km^4)^2]^2#

Use Rule: #(a^m)^n = a^(mn)#

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

#=>(125k^6m^3)[(16k^2m^8)]^2#

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

#=>(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#