How do you simplify #((x^-3 y^-4 )/ (x^-5 y^-7 )) ^-3 #?

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Answer 1 · 2018-03-03T20:24:22

See a solution process below:

First, use this rule of exponents to divide the #x# and #y# terms within the parenthesis:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#((x^color(red)(-3)y^color(red)(-4))/(x^color(blue)(-5)y^color(blue)(-7)))^-3 =>#

#(x^(color(red)(-3)-color(blue)(-5))y^(color(red)(-4)-color(blue)(-7)))^-3 =>#

#(x^(color(red)(-3)+color(blue)(5))y^(color(red)(-4)+color(blue)(7)))^-3 =>#

#(x^color(red)(2)y^color(red)(3))^color(blue)(-3)#

Next, use this rule for exponents to eliminate the outer exponent:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#

#x^(color(red)(2)xxcolor(blue)(-3))y^(color(red)(3)xxcolor(blue)(-3)) =>#

#x^color(red)(-6)y^color(red)(-9)#

Now, use this rule of exponents to eliminate the negative exponents:

#x^color(red)(a) = 1/x^color(red)(-a)#

#1/(x^color(red)(- -6)y^color(red)(- -9)) =>#

#1/(x^color(red)(6)y^color(red)(9))#