Simplify. Write each answer in scientific notation.
1.) (3 * 10^5)^2
2.) (3.5 * 10^ -4) ^3
1. 9*10^10
2. 4.2875*10^-11
Thank you!
but i do have a question. would it be raised to the -12 power? in #2
To simplify and write each answer in scientific notation, we need to perform the given calculations and express the results in the form of a number multiplied by a power of 10.
1.) (3 * 10^5)^2:
Step 1: Square the base number without considering the exponent.
(3 * 10^5) * (3 * 10^5)
Step 2: Multiply the numbers with the same base and add the exponents together.
3 * 3 * 10^5 * 10^5
9 * 10^(5+5)
9 * 10^10
Therefore, (3 * 10^5)^2 can be simplified as 9 * 10^10.
2.) (3.5 * 10^ -4)^3:
Step 1: Cube the base number without considering the exponent.
(3.5 * 10^-4) * (3.5 * 10^-4) * (3.5 * 10^-4)
Step 2: Multiply the numbers with the same base and add the exponents together.
3.5 * 3.5 * 3.5 * 10^-4 * 10^-4 * 10^-4
42.875 * 10^(-4-4-4)
42.875 * 10^-12
Step 3: Convert the decimal number to scientific notation.
4.2875 * 10 * 10^-12
4.2875 * 10^(-12+1)
4.2875 * 10^-11
Therefore, (3.5 * 10^-4)^3 can be simplified as 4.2875 * 10^-11.