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how do you multiply scientific notation with unlike terms

Mathematics
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Just multiply the first term of the notation like; \[(2.5*10^6) * 5 = 1.25*10^7\] When the first term gets over 10 you add on 10 to the exponent
what it if it is like this: 4.2x10^2 x 2.3x10^-3? What would the exponent be? positive or negative?
Using the exponent rules, \[x^a \times x^b = x ^{a+b}\] So the answer is \[(4.2*2.3) * 10 ^{2+(-3)} = 9.88*10^{-1}\]

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Other answers:

are u still going to abide to the laws of exponents?
When using scientific notation the laws of exponents are crucial. Some examples: \[(2 * 10 ^2)*2 = (2*2) * 10^2 \] \[(4*10^5)* 10^4 = 4 *(10^5*10^4) = 4* 10^{5+4} = 4 * 10^9\]
Do you see the pattern?

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