Sure, let's solve this step by step:
Step 1: Understand the Question
We're given the pair of numbers (9.75 x 10³) and (8.4 x 10⁻⁶) and we need to find their product.
Step 2: Rewrite with Similar Bases
We can rewrite this numerical expression as follows:
(9.75 x 10³)(8.4 x 10⁻⁶) = 9.75 * 10³ * 8.4 * 10⁻⁶
Step 3: Use Exponentiation Rule
Next, we apply the rule of exponents which states that when multiplying two exponential expressions with the same base, we have to add the exponents. In the case where one of the exponents is negative, it implies that we are dealing with a fraction, and the operation to be carried out becomes subtraction, not addition.
So we have: 9.75 * 10³ * 8.4 * 10⁻⁶ = 9.75 * 8.4 * 10⁽³−⁶⁾
Step 4: Calculate
Now we calculate each part separately:
9.75 * 8.4 = 81.9
10⁽³−⁶⁾ = 10⁻³ = 0.001
Step 5: Multiply to Get the Final Result
The final step is to multiply these two results together, 81.9 * 0.001 = 0.0819.
So the product of (9.75 x 10³) and (8.4 x 10⁻⁶) is 0.0819.