Question

Evaluate
(49/100)^-(1/2)

Answer 1

`(10)/(7)`

Explanation:

To solve this problem, we first have to understand some exponent rules.

Exponent Rules

1. When an exponent is a fraction, the exponent's numerator is how many instances of the base there are, and its denominator is the root of those instances.

For example,

`5^(2/3) = \sqrt[3]{5^2} = \sqrt[3]{25}`

2. When an exponent is negative, the resulting value is reciprocated.

For example,

`3^(-2) = (1)/(3^2) = (1)/(9)`

Solution

Using these rules, we can rewrite the given expression.

`\left((49)/(100)\right)^(-1/2) = \frac{1}{\sqrt{(49)/(100)}}`

Then, we can simplify the denominator by solving for the square root of the fraction 49/100.

`\frac{1}{\sqrt{(49)/(100)}} = (1)/((7)/(10))`

Finally, we can apply the fraction division rule.

`A / (B)/(C) = A * (C)/(B)`

`(1)/((7)/(10)) = 1 \cdot (10)/(7) = (10)/(7)`