Question

How do you simplify `(2a^[2] b^[-3])^3/ (9a^[-3] b^[2]) ^-1/2`?

Answer 1

Let's just bear in mind three important laws of exponents:

• `a^n/a^m=a^n-m`

• `(a^n)^m=a^n*m`

• `a^-n=1/a^n`

Now, let's proceed:

`(2^3*a^(2*3)b^((-3)*3))/(9^(-1)*a^((-3)(-1))*b^(2(-1)))/2`

`((2^3a^6b^-9)/(9^(-1)a^3b^-2))/2=((8a^3b^(-7))/(1/9))/2=(72a^3b^-7)/2=(36a^3)/b^7`