Final answer:
The value of c in the equation 0.0086 = 8.6 × 10^c is -3, arrived by expressing 0.0086 in scientific notation as 8.6 × 10^-3.
Step-by-step explanation:
To solve for the value of c in the equation 0.0086 = 8.6 × 10c, we need to express 0.0086 in scientific notation. Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
The number 0.0086 can be written as 8.6 × 10-3 because we have moved the decimal point 3 places to the right to get from 0.0086 to 8.6. Now, by comparing this expression with our original equation, 0.0086 = 8.6 × 10c, we can see that the exponent for 10 must be -3 in order to make the expressions equivalent.
Therefore, the value of c is -3.