How do you multiply and simplify #(\frac { 5x ^ { 9} } { 4y ^ { 6} } ) ^ { 4} \cdot ( \frac { 4^ { 3} y ^ { 7} } { 5^ { 2} x ^ { - 3} } )#?

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Answer 1 · 2016-11-23T13:49:04

#(25x^(39))/(4y^(17))#

First, simplify the left term:

#((5^4x^(9*4))/(4^4y^(6*4))) * ((4^3y^7)/(5^2x^-3))#

#((5^4x^(36))/(4^4y^(24))) * ((4^3y^7)/(5^2x^-3))#

Next, combine or multiply the numerator and the denominator:

#(5^4x^(36)4^3y^7)/(4^4y^(24)5^2x^-3)#

Next group like terms and simplify using the rules for exponents:

#(5^4 4^3x^36y^7)/(5^2 4^4x^-3y^24)#

#(5^(4-2)x^(36+3))/(4^(4-3)y^(24-7))#

#(5^(2)x^(39))/(4^(1)y^(17))#

#(25x^(39))/(4y^(17))#