How do you simplify #(\frac { 4m ^ { 6} n ^ { 7} } { 8n ^ { 4} } ) ^ { 3}#?

1 Answer
Jun 12, 2017

#1/8 (m^18n^9)#

Explanation:

Step 1. Distribute the power of #3# to the numerator and denominator

#((4m^6n^7)^3)/((8n^4)^3)#

#(4^3m^18n^21)/(8^3n^12)#

#(64m^18n^21)/(512n^12)#

Step 2. Subtract like powers in numerator and denominator

#(64m^18n^(21-12))/512#

#(m^18n^9)/8#

#1/8 (m^18n^9)#