is x to the 4th power plus x to the 4th power equal to x to the 8th power?
NO!!!
x^4 + x^4
is two x^4 terms
in other words
2 x^4
but
x^4 * x^4 = x^(4+4) = x^8
No, x to the 4th power plus x to the 4th power is not equal to x to the 8th power.
To understand why, let's simplify the equation step by step:
We can rewrite x to the 4th power as (x * x * x * x).
So, x to the 4th power plus x to the 4th power becomes:
(x * x * x * x) + (x * x * x * x).
When we combine like terms, we add the coefficients (which in this case is 1 for both terms):
1 * (x * x * x * x) + 1 * (x * x * x * x).
Simplifying further, we get:
(x * x * x * x) + (x * x * x * x).
Since the terms are the same, we can combine them into one term by adding the coefficients:
2 * (x * x * x * x).
So, x to the 4th power plus x to the 4th power is equal to 2 multiplied by x to the 4th power.
Therefore, the equation simplifies to:
2 * (x * x * x * x).
This is not equal to x to the 8th power, which would be represented as (x * x * x * x * x * x * x * x).