In mathematics there is a rule of exponents where we can "distribute" the powers/exponents in the numerator and denominator of any expression. Therefore, given an expression as , the exponent n can be "distributed" as:
.
In our case, the power, n=11; a=7 and b=4. Thus, the expression , can be written as
.
Thus, out of the given options, option A is the correct option.
Option A:
The shortest distance Mark can cover to reach home early is 54.7 miles.
Solution:
Towards North = 35 miles
Towards West = 42 miles
Using Pythagoras theorem,
<em>In right triangle, squares of the hypotenuse is equal to the sum of the squares of the other two sides.</em>
Let x be the hypotenuse.
Taking square root on both sides, we get
x = 54.67
x = 54.7
The shortest distance Mark can cover to reach home early is 54.7 miles.
Option A is the correct answer.