Question

9^(x/2)

Answer 1

\[9^{x/2}\]

Answer 2

and what you need here ?

Answer 3

I am confused as to how problems like this simplify...
I know that it simplifies to 3^x... but how does that work?

Answer 4

Are you typing something Calcmathlete?

Answer 5

\[9^{\frac{x}{2}} = (\sqrt{9})^{x} = 3^{x}\]

Answer 6

So that is a true statement for any power problem?

Answer 7

Well, are you familiar with turning fractional exponents to radicals?

Answer 8

\[a ^{m/n} = \sqrt[n]{a}^{m}\]

Answer 9

Yes, I am familiar. I am in calculus 2... I wasn't sure if that rule would apply to a base if it had a variable as an exponent.

Answer 10

It still works.

Answer 11

ok. so... 16^x/4 = 2^x?

Answer 12

Yeah.
\[\sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}\]

Answer 13

This problem arose from an integral.

\[\int\limits_{-2}^{2}9^{x/2} dx\]

so that is the same as...
\[\int\limits_{-2}^{2}3^{x} dx\]?