Answer:
D. The number will be less than 1 because when adding the exponents,
11 + (-14) = -3, and a number in scientific notation with a negative exponent is less than 1.
Step-by-step explanation:
The question lacks appropriate option. Find the options below;
A. The value will be greater than 1 because 4.296 x 10^11 is a very large number and multiplication always increases the size of a number.
B. The value will be greater than 1 because 4 x 2 = 8 and 8 is larger than 1.
C. The value will be less than 1 because (4.296 x 10^11) x (1.8614 x 10^-14) will be a negative number. All negative numbers are less than one.
D. The number will be less than 1 because when adding the exponents,
11 + (-14) = 3, and a number in scientific notation with a negative exponent is less than 1.
Given the expression
, to expand the expression we will apply some of the law of indices below. If a, b and m are integers
![a^m*a^n = a^{a+m}](https://tex.z-dn.net/?f=a%5Em%2Aa%5En%20%3D%20a%5E%7Ba%2Bm%7D)
![= (4.296*10^{11})(1.8614*10^{-14})\\\\= (4.296*1.8614)(10^{11}*10^{-14}) \\\\= 7.9965744 * 10^{11}*10^{-14}\\sum \ up \ the\ power\ of\ the \ exponents\\\\= 7.9965744 *10^{11-14}\\\\= 7.9965744 *10^{-3}\\](https://tex.z-dn.net/?f=%3D%20%284.296%2A10%5E%7B11%7D%29%281.8614%2A10%5E%7B-14%7D%29%5C%5C%5C%5C%3D%20%284.296%2A1.8614%29%2810%5E%7B11%7D%2A10%5E%7B-14%7D%29%20%5C%5C%5C%5C%3D%207.9965744%20%2A%2010%5E%7B11%7D%2A10%5E%7B-14%7D%5C%5Csum%20%5C%20up%20%5C%20the%5C%20%20power%5C%20of%5C%20the%20%5C%20exponents%5C%5C%5C%5C%3D%20%207.9965744%20%2A10%5E%7B11-14%7D%5C%5C%5C%5C%3D%207.9965744%20%2A10%5E%7B-3%7D%5C%5C)
= 0.0079965744
<em>Based on the result, it can be seen that the resulting value is less than 1 due to the negative power of its exponent (i.e -3). Any scientific notation having a negative exponent always returns a value that is less than 1.</em>