when adding and subtracting numbers in scientific notation the power of the base 10 must be the same exponent so that you have like terms. when multiplying and dividing numbers in scientific notation you do not have the same power of the base 10. you can simply follow the exponent rule for multiplying and dividing with the like base 10
For addition and subtraction in scientific notation, you need to ensure that the exponents of the base 10 are the same. For example, if you have $3.5 \times 10^{4}$ and $2.7 \times 10^{3}$, you can rewrite them as $0.35 \times 10^{5}$ and $0.27 \times 10^{5}$. Now that they have the same exponent, you can add them together: $0.35 \times 10^{5} + 0.27 \times 10^{5} = 0.62 \times 10^{5}$.
For multiplication and division in scientific notation, you can simply follow the exponent rule for like base 10. For example, if you have $(3.5 \times 10^{4})(2.7 \times 10^{3})$, you can multiply the numbers together: $(3.5 \times 2.7) \times 10^{4+3} = 9.45 \times 10^{7}$.
Similarly, if you have $\frac{3.5 \times 10^{4}}{2.1 \times 10^{2}}$, you can divide the numbers and subtract the exponents: $\frac{3.5}{2.1} \times 10^{4-2} = 1.67 \times 10^{2}$.