Question

4x 10⁷ is _____ times as much as 4 x 10³.

a) 10¹⁰
b) 4 * 10¹⁰
c) 4 * 10⁴
d) 10⁴

Answer 1

4 x 10⁷ is 10⁴ times as much as 4 x 10³, as simplifying the division of the two expressions shows that the coefficients cancel out and the powers of 10 subtract, giving us 10⁴.

Step-by-step explanation:

To determine how many times 4 x 10⁷ is as much as 4 x 10³, we can simplify the problem by dividing the former by the latter:

1. (4 x 10⁷) / (4 x 10³)
2. This can be rewritten as 4/4 x 10⁷/10³ since the properties of exponents allow us to divide the coefficients (4/4) and the powers of ten separately.
3. The division 4/4 equals 1, and for the powers of 10, we subtract the exponents due to the laws of exponents: 10⁷/10³ = 10⁷-³ = 10⁴.
4. Therefore, the simplified form is 1 x 10⁴, which means 4 x 10⁷ is 10⁴ times as much as 4 x 10³.

The correct answer is d) 10⁴.