Radicals and Rational Exponents

[gadawgs3]

I need help solving this problem. I am trying to write d in terms of A and S.

S = 16Ad^(-2/3)

This is what I have so far:

I divided both sides by 16A
Multiplied both sides by -3/2
Flipped the base in order to remove the negative exponent

16A^3/2 = d
S^3/2

 

[srmichael]

I need help solving this problem. I am trying to write d in terms of A and S.

S = 16Ad^(-2/3)

This is what I have so far:

I divided both sides by 16A
Multiplied both sides by -3/2
Flipped the base in order to remove the negative exponent

16A^3/2 = d
S^3/2

Close. You forgot to make sure that the 16 is raised to the 3/2 power as well. A common mistake that is made. Thus:

\(\displaystyle d=(\frac{16A}{S})^\frac{3}{2}=\frac{(16^\frac{3}{2})(A^\frac{3}{2})}{S^\frac{3}{2}}=64(\frac{A}{S})^\frac{3}{2}\)