91Ó°ÊÓ

In algebra, we often work with numbers that have both a base and an exponent. The base is the number that is being multiplied, and the exponent tells us how many times the base is multiplied by itself.
For example, in the expression \(x^3\), \(x\) is the base, and 3 is the exponent. This means \(x\) is multiplied by itself 3 times: \(x \times x \times x\).
Understanding bases and exponents makes it easier to perform calculations and simplify expressions. When dealing with multiple bases and exponents, make sure to first identify each base and its corresponding exponent. In our example problem, we have the terms \(-x^3\) and \(x^4\). Here, both terms share the same base, \(x\), with exponents 3 and 4 respectively.

When multiplying expressions that have the same base, there is a simple rule to follow: add the exponents. This rule works because you are essentially extending the multiplication process.
For instance, consider the product \(x^3 \times x^4\). The base \(x\) is the same in both terms. According to the multiplication rule for exponents, you add the exponents: \(3 + 4\). This gives us \(x^{3+4} = x^7\).
In our example problem, we apply this rule to the expression \(-x^3 \times x^4\). We first identify the common base \(x\) and then add the exponents (3 + 4). This results in the new expression \(-x^7\). It's important to keep the same base and simply add the exponents together.

Once you've applied the multiplication rule for exponents, the final step is to simplify the expression. Simplifying involves reducing the expression to its simplest form.
In our problem, after adding the exponents (3 + 4), we get \(-x^7\).
To simplify exponents, ensure there are no further operations or factors to combine. In this case, \(-x^7\) is already in its simplest form because there's nothing left to multiply or add. Simplification makes it easier to interpret and work with expressions, ensuring they are as straightforward as possible.
Always double-check your work to make sure that all operations have been correctly applied and that the expression is indeed simplified.