Final answer:
The expression (-1)^4 x (-1)^9 simplifies to (-1)^13, because when multiplying powers with the same base, the exponents are added together.
Step-by-step explanation:
When multiplying powers with the same base, you can simply add the exponents. In this case, we are dealing with a base of -1. The expression (-1)^4 x (-1)^9 can be simplified by adding the exponents 4 and 9 together, which equals 13. Therefore, (-1)^4 x (-1)^9 equals (-1)^13.
The reason behind this is that integer powers are a way of indicating that a number is to be multiplied by itself a certain number of times. For example, 4³ is shorthand for 4 x 4 x 4. Similarly, negative exponents signify that the base is in the denominator; for example, x^-1 equals 1/x. In our case, (-1) raised to an odd power, such as 13, will always result in -1, given the nature of negative numbers multiplied by themselves.