Question

How do you simplify `9times10^ -31 * (3times10 ^7)^2`?

Answer 1

`81 * 10^(-17)`

Explanation:

First of all, simplify the square in the second part:

`9 * 10 ^(-31) * (3 * 10^7)^2 = 9 * 10^(-31) * 3^2 * (10^7)^2`

According to the power rule `(a^n)^m = a^(n*m)`, you can simplify further:

`... = 9 * 10^(-31) * 9 * 10^14`

Now, compute `9 * 9`:

`... = 81 * 10^(-31) * 10^14`

Use the power rule: `a^n * a^m = a^(n+m)`

`... = 81 * 10^(-31 + 14) = 81 * 10^(-17)`

This might already be a final answer.

If you would like to formulate the result in the scientific notation, you would need to shift one digit of the `81` and thus increase the exponent of the basis `10` by `1`:

`... = 8.1 * 10^(-16)`.