Answer: To subtract these two numbers written in scientific notation, you first need to ensure that they have the same exponent (power of 10). To do this, you can rewrite each number so that they have the same exponent.
[tex]\(4.6 \times 10^2\)[/tex] can be rewritten as [tex]\(460 \times 10^0\)[/tex] since [tex]\(10^2 = 100\)[/tex] and [tex]\(100 \times 4.6 = 460\)[/tex].
[tex]\(3.5 \times 10^3\)[/tex] can be rewritten as [tex]\(3500 \times 10^0\)[/tex] since [tex]\(10^3 = 1000\)[/tex] and [tex]\(1000 \times 3.5 = 3500\)[/tex].
Now, you can subtract the two numbers:
[tex]\[460 \times 10^0 - 3500 \times 10^0 = (460 - 3500) \times 10^0\]\[= -3040 \times 10^0\][/tex]
Since [tex]\(10^0 = 1\)[/tex] you're left with [tex]\( -3040 \times 1 = -3040\)[/tex].
So, [tex]\(4.6 \times 10^2 - 3.5 \times 10^3 = -3040\)[/tex].
