What is the product of x^a and x^b according to exponent rules?

The product of ( x^a ) and ( x^b ) follows the exponent rule that states when multiplying two expressions with the same base, you add the exponents. This can be represented mathematically as:

[ x^a \times x^b = x^{(a + b)}

]

In this case, the base ( x ) is the same in both terms, and you simply combine the powers by adding ( a ) and ( b ). Therefore, the product results in ( x ) raised to the sum of the exponents ( a ) and ( b ).

This concept is essential in algebra and is widely applicable in various mathematical contexts, including polynomial multiplication, simplifying expressions, and solving equations involving exponentials. The understanding that the same bases add their exponents in multiplication is foundational in working with powers and can be seen in most algebraic operations involving exponents.