The product of 1.7 × 10⁴ and 12.5 × 10⁻⁶ is expressed in the standard form as k × 10ⁿ. The value of (2k + n) is

The correct answer is 3.25.

Step 1: Calculate the product of the given numbers.
We need to find the product of 1.7 × 10⁴ and 12.5 × 10⁻⁶.

Multiply the decimal numbers and combine the powers of 10 using exponent rules:

$\text{Product}=(1.7\times 12.5)\times ({10}^4\times {10}^{-6})$

Calculating 1.7 × 12.5:
1.7 × 12.5 = 21.25

Calculating 10⁴ × 10⁻⁶ using the rule 10^a × 10^b = 10^a+b:
10⁴ × 10⁻⁶ = 10^{4 + (-6)} = 10⁻²

So, the product is 21.25 × 10⁻².

Step 2: Express the result in standard form (k × 10ⁿ).
In standard scientific notation k × 10ⁿ, the value of k must satisfy 1 ≤ k < 10.

Convert 21.25 to standard form:
21.25 = 2.125 × 10¹

Now substitute this back into the expression:

$21.25\times {10}^{-2}=(2.125\times {10}^1)\times {10}^{-2}=2.125\times {10}^{1-2}=2.125\times {10}^{-1}$

Comparing 2.125 × 10⁻¹ with k × 10ⁿ:
k = 2.125
n = -1

Step 3: Evaluate (2k + n).
Substitute the values of k and n into the expression (2k + n):

$2k+n=2\left(2.125\right)+(-1)$

2 × 2.125 = 4.25
4.25 + (-1) = 3.25

Thus, the value of (2k + n) is 3.25.