How do you evaluate and simplify #9/9^(-4/5)#?

Question

3328 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-09T12:59:21

See a solution process below:

First, use this rule of exponents to eliminate the negative exponent:

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

#9/9^color(red)(-4/5) = 9 * 9^color(red)(- -4/5) = 9 * 9^(4/5)#

Next, use these rules to combine the 9's terms:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#9 * 9^(4/5) => 9^color(red)(1) * 9^color(blue)(4/5) => 9^(color(red)(1)+color(blue)(4/5)) => 9^(color(red)(5/5)+color(blue)(4/5)) =>#

#9^(9/5)#

Answer 2 · 2017-07-09T16:26:53

#:.color(blue)(=52.196# to the nearest 3 decimal places

#9/(1/9^(-4/5))#

#:.1/a^-2=a^2#

#:.=9/(1/9^(4/5))#

#:.=9/1 xx 9^(4/5)/1#

#:.=9^(5/5) xx 9^(4/5)#

#:.=9^(9/5)#

#:.=root5(9^9)#

#:.=root5(9*9*9*9*9*9*9*9*9)#

#:.root5(9)*root5(9)*root5(9)*root5(9)*root5(9)=9#

#:.=9root5(9*9*9*9)#

#:.=9root5(3*3*3*3*3*3*3*3)#

#:.root5(3)*root5(3)*root5(3)*root5(3)*root5(3)=3#

#:.=3*9root5(27)#

#:.=27root5(27)#

#:.=52.19591521#

#:.color(blue)(=52.196# to the nearest 3 decimal places