Question

When dividing two exponential expressions of the same nonzero​ base, what should you do to their exponents, and how should you use this difference as the exponent of the common base?

Answer 1

To divide exponential expressions with the same base, subtract the lower exponent from the higher one. The result is the new exponent of the common base. Coefficients are divided normally, and if needed, adjust the result to standard form.

Step-by-step explanation:

When dividing two exponential expressions with the same nonzero common base, you should subtract the exponent of the denominator from the exponent of the numerator. This difference becomes the exponent of the result, which is still expressed with the common base. For example, if you have √ 10^6 / 10^3, you would calculate 10^(6-3) which equals 10^3. When working with the coefficients in front of the exponential terms, you divide them just like any other numbers.

Remember, if the result of this division gives you a number that does not conform to standard form (a number between 1 and 10), you must adjust it. For instance, if you had a coefficient of 24, you would convert this to 2.4 and increase the exponent by one to maintain the equality.