Final answer:
Any number, except zero, raised to any positive integer power retains that number's value, and for number 1 specifically, it always equals 1, regardless of the exponent. For instance, 1⁸ is equal to 1.
Step-by-step explanation:
The power that has the same value as 1⁸ is 1. In mathematics, when we raise any number to an integer power, we are essentially multiplying that number by itself multiple times. However, any number (except for zero) raised to the eighth power is simply that number multiplied by itself seven more times. In this particular case, we have the number 1 being multiplied by itself multiple times.
Now, the unique property of the number 1 is that it is the multiplicative identity, meaning it stays the same when multiplied by any number, including itself. Therefore, regardless of the exponent, as long as it’s a positive integer, 1 raised to any power, such as 1², 1³, 1⁴, and so on, will always result in 1.
An easy way to remember this is whenever you see an expression like 1 to the power of any positive integer, you can confidently say the result is 1. This is because 1 is the only number that, when multiplied by itself, does not change in value. Hence, 1⁸ is equal to 1.