Do you need the powers to be the same to multiply/divide in scientific notation?
No, you do not need the powers to be the same in order to multiply or divide numbers in scientific notation.
When multiplying, you multiply the coefficients (the numbers before the power of 10) and add the exponents together. This creates a new power of 10 that represents the overall magnitude of the result.
When dividing, you divide the coefficients and subtract the exponents. This also creates a new power of 10 that represents the overall magnitude of the result.