What is the result of multiplying x to the power of a by x to the power of b?

When multiplying two expressions that have the same base, the rule of exponents states that you add the exponents. In this case, you have x raised to the power of 'a' and x raised to the power of 'b'. According to the exponent multiplication rule, when you multiply these two expressions together, you combine the exponents:

[

x^a \cdot x^b = x^{a+b}

]

This means that the result of multiplying x to the power of a by x to the power of b is indeed x raised to the power of the sum of the two exponents, which is 'a + b'. This is a fundamental property of exponents and holds true for any real numbers 'a' and 'b'.

The other potential choices represent incorrect operations or interpretations of exponent multiplication. For instance, subtracting exponents, multiplying them directly together, or considering them in a multiplication context in other manners doesn’t apply here. Therefore, the only valid answer that accurately describes the operation of multiplying the two expressions is x to the power of a plus b.