OK I need help with this problem I am trying to figure out exactly where I have gone wrong with it I am not sure even if I have done it right

Evaluate and simplify; express answer with only positive exponents. (25a^8b^16)^-1/2

now I don't see where I can make the check mark thingie for sqrt... so I will try to do my best here with what I have so far..

Ö25*a^2*a^2*a*2*a^2*b^16 factor a^8 into a^2*a^2*a^2*a^2

Ö25*a^2*a^2*a*2*a^2*b^2*b^2*b^2*b^2*b^2*b^2*b^2*b^ 2 factor b^16 into

b^2*b^2*b^2*b^2*b^2*b^2*b^2*b^2

OK so here's were I feel I am doing this wrong cause it makes no sense so I have stopped and need help with this problem.Thanks for your help in advance

Oh Gosh...

Put it simpler:

(25a^8b^{16})^-{\frac{1}{2}} = (25)^-{\frac{1}{2}}(a^8)^-{\frac{1}{2}}(b^{16})^-{\frac{1}{2}} = (\frac{1}{5})(a^{-4})(b^{-8})

How did I do that you may ask, I'll show you;

(a^2)^2 = (a \times a )^2 = (a\times a)(a\times a) = (a\times a \times a \times a) = a^4

So, if you have two powers, you multiply them.

See, (a^2)^2? Multiply 2 and 2, keeping a as it is.

Now, if it's a negative, keep the same rule;

(a^3)^{-2} = a^{(3 \times -2)} = a ^{-6}

Got it?

I hope that helped! :)