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When you multiply exponents with the same base, you add their exponents. This rule helps in simplifying expressions where the same base is repeatedly multiplied. For example, in the given exercise, you have to multiply \(d^7\) and \(d^6\) which has the same base \(d\). To multiply these, you add the exponents: \(7 + 6\). This results in \(d^{13}\).

You can remember this rule with the simple phrase: 'When multiplying, you add'. It's a handy trick and will make your calculations much faster.

Dividing exponents involves a different rule. When you divide exponents with the same base, you subtract the exponent of the denominator from the exponent of the numerator. This helps in simplifying expressions where one exponent is divided by another with the same base.

In the given exercise, after multiplying the exponents, the fraction can be written as \(\frac{d^{13}}{d^{12}}\). When dividing like bases, you subtract the exponents: \(13 - 12 = 1\). This simplifies to \(d^1\), which is simply \(d\).

An easy way to remember this rule is: 'When dividing, you subtract'. This will keep your computations correct and easy!

The rules for multiplying and dividing exponents only work when the bases are the same. In the exercise, the base is \(d\) in all parts of the expression. That consistency allows the use of the addition and subtraction rules for exponents.

If the bases were different, you could not combine the exponents in this way. For instance, \(d^7\) and \(e^6\) cannot be combined because their bases ( \(d\) and \(e\)) aren’t the same.

Always check if the bases match before applying these rules. Remember, 'Like bases let you add or subtract exponents' - it’s a key concept whenever you deal with exponents.
Understanding these foundational rules will make simplifying exponents much easier and straightforward. Enjoy practicing them in your exercises!