Which of these is correct?(1 point)

Question

Responses

(9.9 × 10^7)(5.8 × 10^6) = 5.72 × 10^13
open paren 9 point 9 times 10 to the 7th power close paren times open paren 5 point 8 times 10 to the 6th power close paren is equal to 5 point 7 2 times 10 to the 13th power

(2.9 × 10^8)(1.3 × 10^7) = 3.77 × 10^15
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 × 10^8)(4.2 × 10^7)=13 × 10^15
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

(4.6 × 10^5)(2.1 × 10^4) = 2.5 × 10

Answer 1

Let's evaluate each expression step by step.

1. (9.9 × 10^7)(5.8 × 10^6):

   • Coefficients: \(9.9 \times 5.8 = 57.42\)
   • Exponents: \(10^7 \times 10^6 = 10^{7+6} = 10^{13}\)
   • Result: \(57.42 \times 10^{13}\), which can be expressed as \(5.742 \times 10^{14}\) (after adjusting the coefficient).

2. (2.9 × 10^8)(1.3 × 10^7):

   • Coefficients: \(2.9 \times 1.3 = 3.77\)
   • Exponents: \(10^8 \times 10^7 = 10^{15}\)
   • Result: \(3.77 \times 10^{15}\). This is correct.

3. (8.8 × 10^8)(4.2 × 10^7):

   • Coefficients: \(8.8 \times 4.2 = 37.76\)
   • Exponents: \(10^8 \times 10^7 = 10^{15}\)
   • Result: \(37.76 \times 10^{15}\), which can be expressed as \(3.776 \times 10^{16}\) (after adjusting the coefficient). Thus, it's incorrect as the provided answer is \(13 \times 10^{15}\).

4. (4.6 × 10^5)(2.1 × 10^4):

   • Coefficients: \(4.6 \times 2.1 = 9.66\)
   • Exponents: \(10^5 \times 10^4 = 10^{9}\)
   • Result: \(9.66 \times 10^{9}\), which is not equal to \(2.5 \times 10\).

In summary, the only correct statement among the options provided is:

(2.9 × 10^8)(1.3 × 10^7) = 3.77 × 10^15.