How to simplify this?

Question

#(16/(9x^4))^(-(3/2))#

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Answer 1 · 2017-03-30T07:17:07

The value of this expression is:

#(16/(9x^4))^(-3/2)=((9x^4)/16)^(3/2)=((3x^2)/4)^3=(27x^6)/64#

In the first step I used the rule that:

The second step is :

Final step is just calculating the cube (third power) of the expression

Answer 2 · 2017-03-30T08:54:36

#color(red)((27x^6)/64#

#(16/(9x^4))^-(3/2)#

#:.=(4^2/(3^2x^4))^-(3/2)#

#:.=(4^(2 xx -3/2))/(3^(2 xx -3/2)x^(4 xx -3/2)#

#:.=(4^(-6/2))/(3^(-6/2)x^(-12/2))#

#:.=(4^-3)/(3^-3 x^-6)#

#:.=(1/4^3)/(1/3^3*1/x^6)#

#:.=1/4^3 xx 3^3/1 xx x^6/1#

#:.=color(red)((27x^6)/64#