Final answer:
The expression that is 3 × 10⁷ times as great as 2x10⁻⁴ is 6x10³, found by multiplying the coefficients (getting 6) and adding the exponents of ten (getting an exponent of 3).
Step-by-step explanation:
The student is asking which expression is 3 × 10⁷ times as great as 2x10⁻⁴. To find the expression that is a multiple times greater than another, we simply multiply the given number by that multiple. Using scientific notation, we multiply the coefficients and add the exponents when multiplying powers of ten.
Starting with the expression 2x10⁻⁴, we want to find what is equal to 3 × 10⁷ times this amount. Multiplying the coefficients we get 3 × 2 = 6. Then we add the exponents of ten, which in this case are 7 (from the 10⁷) and -4 (from the 10⁻⁴).
Adding 7 and -4 gives us an exponent of 3. So, the resulting expression is 6x10³. This expression is 3 × 10⁷ times as great as 2x10⁻⁴.