Final answer:
To simplify the given expression in scientific notation, multiply the coefficients (9 and 3) to get 27, and then add the exponents (13 and 10) to get 23, resulting in the simplified expression 27 x 10^23.
Step-by-step explanation:
To simplify the expression (9x10¹³)(3x10¹°), we follow the rule for multiplying numbers in scientific notation. This rule states that we should multiply the coefficient numbers (the numbers in front of the powers of ten) together, and then add the exponents of the tens. In this case:
- Multiply the coefficients: 9 * 3 = 27
- Add the exponents: 10¹³ + 10¹° = 10¹³¹° (since the bases are the same, you add the exponents)
The final result is 27 x 10²³, which is the simplified form of the original expression.