The given expression is
[tex] -(\frac{49}{64} )^{1/2} [/tex]
49 is the square of 7 and 64 is the square of 8.
So we can write the given expression as
[tex] -(\frac{7^2}{8^2})^{1/2} [/tex]
[tex] =-(\frac{7}{8})^{2*1/2} = -\frac{7}{8} [/tex]
Rational expressions work like this: if you raise a number x to the power m/n, it means that you're considering the n-th root of x^m.
So, in this case, you are considering the second root (i.e. the square root) of 49/64 to the first power, i.e. 49/64 itself. In formula, you have
[tex] \left(\cfrac{49}{64}\right)^{\frac{1}{2}} = \sqrt{\cfrac{49}{64}} = \cfrac{\sqrt{49}}{\sqrt{64}} = \cfrac{7}{8} [/tex]
Since there is a minus sign in front of the whole expression, the answer is -7/8
