Question

what is the exponent form of sqrt (x^3) ?

Answer 1

\[ \sqrt{y} = y^{1/2} \]
hence
\[ \sqrt{x^3} = (x^3)^{1/2} = x^{3/2} \]

Answer 2

yes that's what i got. but if i substitute x=8, the answer for using sqrt (x^3) and x^3/2 is different

Answer 3

cuz i am suppose to find the slope of the tangent at x=8, which the answer is 3 sqrt 2, but i couldnt get the answer using power rule

Answer 4

No so. \( 8^3 = 512 \) and \( \sqrt{512} = 16 \sqrt{2} \), while ...

Answer 5

\( 8^{3/2} = (2^3)^{3/2} = 2^{9/2} = 2^4 \sqrt{2} = 16 \sqrt{2} \)

Answer 6

Got it?

Answer 7

umm, but if i do the power rule
y' = 3/2 (8) ^1/2

i got some decimal answers

Answer 8

Ok, now you have
\[ y' = \frac{3}{2} \sqrt{8} = \frac{3}{2} 2 \sqrt{2} = 3\sqrt{2} \]

Answer 9

ohh ok i get it now. so i just cant plug everything in the calculater

Answer 10

If you started with \( y = \sqrt{x^3} \) and evaluate this with the chain rule, then
\[ y' = 3x^2 \cdot \frac{1}{2} \frac{1}{\sqrt{x^3}} \] Work this through, and you'll find it equal to what's above.

Answer 11

oh ok i will try it! thanks !