How to simplify this?

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

2 Answers
Mar 30, 2017

Answer:

The value of this expression is:

#(27x^6)/64#

Explanation:

#(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:

#a^-b=1/a^b#

The second step is :

#a^(1/n)=root(n)(a)#

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

Mar 30, 2017

Answer:

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

Explanation:

#(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#