Answer:
(A) 4.03 x 10^14
Step-by-step explanation:
403,000,000,000,000
Scientific notation is of the form
a * 10 ^b
where a is a number from 1 to a number less than 10
Put the decimal in the number
403,000,000,000,000.
We need to move the decimal 14 places to the left to get the number to be between 1 and 10
4.03000000000000 so the b is 14
Since we moved it to the left b is positive
We can drop the extra zeros at the end (after the last nonzero digit)
4.03 *10^14
Answer:
(c) (12th root of 8)^x
Step-by-step explanation:
The applicable rules of exponents are ...
![(a^b)^c=a^{bc}\\\\\sqrt[n]{a}=a^{1 \! /n}](https://tex.z-dn.net/?f=%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D%5C%5C%5C%5C%5Csqrt%5Bn%5D%7Ba%7D%3Da%5E%7B1%20%5C%21%20%2Fn%7D)
In this case, we have ...
![(\sqrt[3]{8})^{x/4}=8^{1/3\cdot x/4}=8^{x/12}=\boxed{\left(\!\sqrt[12]{8}\right)^x}](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B8%7D%29%5E%7Bx%2F4%7D%3D8%5E%7B1%2F3%5Ccdot%20x%2F4%7D%3D8%5E%7Bx%2F12%7D%3D%5Cboxed%7B%5Cleft%28%5C%21%5Csqrt%5B12%5D%7B8%7D%5Cright%29%5Ex%7D)
Answer: All real values of x
Step-by-step explanation:
The absolute value of a real number is always non-negative, and thus must always be greater than any negative number.
