How do you simplify #\frac { ( 6b ^ { 5} d ^ { 8} ) ^ { 3} } { ( 2b ^ { 3} ) ( 4b c ^ { 4} ) }#?

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Answer 1 · 2018-07-25T21:54:34

#{27 b^{11}d^{24}}/c^4#

Given that

#\frac{(6b^5d^8)^3}{(2b^3)(4bc^4)}#

#=\frac{(6)^3(b^5)^3(d^8)^3}{(2\cdot 4)(b^3\cdotb)(c^4)}#

#=\frac{(216)(b^{5\cdot 3})(d^{8\cdot 3})}{(8)(b^4)(c^4)}#

#=\frac{(216)(b^{15})(d^{24})}{(8)(b^4)(c^4)}#

#=(216/8)(b^{15}/b^4)(d^{24}/c^4)#

#=(27)(b^{15-4})(d^{24}/c^4)#

#=27b^{11}(d^{24}/c^4)#

#={27 b^{11}d^{24}}/c^4#