Question

Evaluate the expression -(49/64)^1/2

Answer 1

The given expression is

$-(\frac{49}{64} )^{1/2}$

49 is the square of 7 and 64 is the square of 8.

So we can write the given expression as

$-(\frac{7^2}{8^2})^{1/2}$

$=-(\frac{7}{8})^{2*1/2} = -\frac{7}{8}$

Answer 2

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

$\left(\cfrac{49}{64}\right)^{\frac{1}{2}} = \sqrt{\cfrac{49}{64}} = \cfrac{\sqrt{49}}{\sqrt{64}} = \cfrac{7}{8}$

Since there is a minus sign in front of the whole expression, the answer is -7/8