Question

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

Answer 1

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)^{(1)/(2)} = \sqrt{\cfrac{49}{64}} = \cfrac{√(49)}{√(64)} = \cfrac{7}{8}`

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

Answer 2

The given expression is

`-((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

`-((7^2)/(8^2))^(1/2)`

`=-((7)/(8))^(2*1/2) = -(7)/(8)`