Your calculation is S = (16 Newtons) / ( 9.079×10^ -8 meters^2)
a) S = (16 / 9.079) / 10^ -8 (Newtons) / (meters)^2
b) S = 1.762 / 10^ -8 Nm^-2
c) S = 1.76×10^ 8 Nm^-2
Line a separates numbers from units—but keep track of both! In line b the number is calculated. I round to 4 significant figures to match the given data. In line c I switch a negative exponent denominator to a positive exponent numerator. (Make sense?) Line c also shows the SI abbreviations N for newtons and m for meters & standard notation for “newtons per meter squared.”
Note that 1 Nm^-2 equals 1 Pa (Pascal). The chart posted by @LuckyGuy shows the tensile strength of many materials, reported in MPa (megaPascal = 10^6Pa = 10^6Nm-2) so I guess you’re in the right ballpark numerically as well as unit-wise.
I offer this tip:
Dimensional units multiply & divide & form powers just as numbers do, which provides an important and convenient way to check for calculation errors, multiplying when you should be dividing, etc. For example, driving 50 miles in 2.5 hours is an average speed of:
(50 miles) / (2.5 hours)
= (50/2.5) (miles/hours)
= 20 mph
Note how miles divides by hrs to yield mph. Multiplying instead of dividing would yield units of mi-hr (“mile-hours”), which is meaningless, rather than mi/hr (“miles per hour).
This method works well for complicated calculations involving many unit conversions. For example how many seconds in a year?
1 y = (52 weeks) * (7 days/week) * (24 hours/day) * (60 min/hour) * (60 sec/min)
Now you calculate the numerical product – around 3.1×10^7
Meanwhile you collect the units together, like this
(weeks) * (days/week) * (hours/days) * (minutes/hours) * (seconds/minute)
Most of the units appear once in a numerator & once in a denominator, so they “cancel out.” All that remains unit-wise on the right-hand side of the equation is seconds (not 1/seconds or some other unexpected thing). The final result is 1 year = 3.1×10^7 seconds…and you are confident you multiplied & divided everything correctly because the units worked out exactly as shown.