Question

How to divide exponents with different bases and powers.

Answer 1

To divide exponents with the same base, you divide the coefficients and subtract the exponents. If you have different bases, you need to either convert to the same base or deal with them differently, as the subtraction rule does not apply.

Step-by-step explanation:

When you are dealing with the division of exponentials with different bases and powers, it's necessary to understand that the general rules for exponents only apply when bases are the same. If the bases are different, you can't directly subtract the exponents. However, if you're dealing with the same base, you divide the coefficients (or digit terms) and subtract the exponents of the exponential terms.

Here's one such example:

Given:
106 / 103

To divide these exponents with the same base (10), we subtract the exponent in the denominator (3) from the exponent in the numerator (6). The result is 106-3 = 103.

In cases where coefficients are involved, such as 4.5 × 109 / 10, you would first divide 4.5 by 1 (since 10 can be thought of as 1 × 10), which gives you 4.5, and then subtract the exponent of 10 in the denominator from the exponent of 10 in the numerator, which gives you 4.5 x 108.

Answer 2

When dividing exponents with the same base, the process includes dividing the coefficients and subtracting the exponents. For different bases, the bases must be made the same or dealt with separately. In scientific notation, coefficients are adjusted to be between 1 and 10 by modifying the exponent.

Step-by-step explanation:

When dividing exponents with different bases and powers, the process involves dividing the coefficients (the numbers out front) and subtracting the exponents if the bases are the same. Assuming we're dealing with the same base, here's how you would do it:

• Divide the digit term of the numerator by the digit term of the denominator.
• Subtract the exponents of the exponential terms, but only if the bases are the same.