What is the result of multiplying x^m by x^n?

To understand the result of multiplying ( x^m ) by ( x^n ), we can use the properties of exponents. The key property at play here is that when multiplying two expressions that have the same base, you add their exponents.

In this case, both expressions have the base ( x ). Therefore, when you multiply ( x^m ) by ( x^n ), you combine the exponents as follows:

[

x^m \cdot x^n = x^{m+n}

]

This shows that the correct outcome of the multiplication is indeed ( x^{m+n} ).

This property is foundational in exponent rules and applies universally, which is why it is always essential to remember that when multiplying like bases, you add the exponents.