Power associativity

Power associativity is a rule that helps us solve math problems that involve taking a number to a power, which means multiplying the number by itself a certain number of times.

Let's say you have the problem 2 raised to the power of 3, which is written as 2^3. This means you have to multiply 2 by itself three times:

2 x 2 x 2

= 8

Now, let's say we have another problem: 2 raised to the power of 4, which is written as 2^4. This means we have to multiply 2 by itself four times:

2 x 2 x 2 x 2

= 16

Now, let's say we want to solve the problem of 2 raised to the power of 3, and then take the result and raise it to the power of 4. We can write this as (2^3)^4. To solve this problem, we need to remember the rule of power associativity, which says we can group the numbers differently as long as we multiply everything together in the end.

So, using the rule of power associativity, we can rewrite (2^3)^4 as 2^(3x4) or 2^12. This means we need to multiply 2 by itself 12 times:

2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x2 x 2

= 4,096

So, power associativity is a mathematical rule that allows us to simplify problems that involve taking powers of numbers by grouping the numbers differently without changing the final answer.