What is the value of n in the equation 2.3 × 10^9 = (1 × 10^3)(2.3 × 10^n)?

To solve for ( n ) in the equation ( 2.3 times 10^9 = (1 times 10^3)(2.3 times 10^n) ), we can simplify the right side.

1. Start by distributing ( 1 times 10^3 ):

[

(1 times 10^3)(2.3 times 10^n) = 2.3 times 10^{3+n}

]

2. Now the equation looks like this:

[

2.3 times 10^9 = 2.3 times 10^{3+n}

]

3. Since the coefficients (2.3) on both sides are equal, we can set the exponents equal to each other:

[

9 = 3 + n

]

4. Solve for ( n ):

[

n = 9 – 3 = 6

]

Thus, the value of ( n ) is ( 6 ).