Which of these is correct?(1 point)

Question

Responses
(4.6×105)(2.1×104)=2.5×10
(4.6×105)(2.1×104)=2.5×10

(2.9×108)(1.3×107)=3.77×1015
open paren 2 point 9 times 10 to the 8th power close paren times open paren 1 point 3 times 10 to the 7th power close paren is equal to 3 point 7 7 times 10 to the 15th power

(8.8×108)(4.2×107)=13×1015
open paren 8 point 8 times 10 to the 8th power close paren times open paren 4 point 2 times 10 to the 7th power close paren is equal to 13 times 10 to the 15th power

(9.9×107)(5.8×106)=5.72×1013

Answer 1

To determine which of the given calculations is correct, we need to do the multiplication step-by-step using the properties of scientific notation:

1. (4.6×10^5)(2.1×10^4): \[ (4.6 \times 2.1) \times (10^5 \times 10^4) = 9.66 \times 10^{(5+4)} = 9.66 \times 10^9 \]

2. (2.9×10^8)(1.3×10^7): \[ (2.9 \times 1.3) \times (10^8 \times 10^7) = 3.77 \times 10^{(8+7)} = 3.77 \times 10^{15} \]

3. (8.8×10^8)(4.2×10^7): \[ (8.8 \times 4.2) \times (10^8 \times 10^7) = 37.16 \times 10^{(8+7)} = 37.16 \times 10^{15} \] This is equivalent to \(3.716 \times 10^{16}\) when adjusted to proper scientific notation (dividing by 10 and increasing the exponent by 1).

4. (9.9×10^7)(5.8×10^6): \[ (9.9 \times 5.8) \times (10^7 \times 10^6) = 57.42 \times 10^{(7+6)} = 57.42 \times 10^{13} \] This is equivalent to \(5.742 \times 10^{14}\) when adjusted to proper scientific notation (dividing by 10 and increasing the exponent by 1).

Now let's summarize the results:

1. (4.6×10^5)(2.1×10^4) = 9.66×10^9 (Not correct)
2. (2.9×10^8)(1.3×10^7) = 3.77×10^15 (Correct)
3. (8.8×10^8)(4.2×10^7) = 37.16×10^{15} (Not correct)
4. (9.9×10^7)(5.8×10^6) = 57.42×10^{13} (Not correct)

Final Conclusion: The second expression, \((2.9 \times 10^{8})(1.3 \times 10^{7}) = 3.77 \times 10^{15}\), is the only correct statement.