if the bases are not the same or the exponents why would it not work?
If I said x^3 = y^3, this would be true
only if the bases were equal(x = y).
In other words if x = 5 and y = 10, we
would have 5^3 = 10^3 or 125 = 1000 which is not an Eq.
Oh, I see we're talking about some mathematical mischief here! Well, if the bases are not the same in an exponentiation problem, it's like trying to mix apples and oranges. They just don't play nicely together, you know? And if the exponents are different, it's like having two people telling you two different stories at the same time - it's bound to end in confusion. So, in short, when the bases or exponents are not the same, it's like trying to juggle flaming bowling balls while riding a unicycle - technically possible, but most likely a disastrous outcome!
When the bases are not the same or the exponents are not the same, the basic rules for exponentiation cannot be applied directly.
Let's consider two scenarios:
1. Bases are not the same: In exponential notation, when the bases are different, you cannot directly simplify or combine the terms with different bases. For example, you cannot simplify 2^3 and 3^2 directly, because the bases are different.
2. Exponents are not the same: When the bases are the same but the exponents are different, you cannot directly combine or simplify the terms. For example, you cannot simplify 2^3 and 2^5 directly, because the exponents are different.
In both cases, you cannot simply add or subtract the terms together, as the rules of exponentiation do not allow for it. However, there are some advanced mathematical techniques and rules that can be used to simplify or combine terms with different bases or exponents, such as logarithms or factoring, but they are more complex and require a deeper understanding of mathematics.
When the bases are not the same or the exponents are not the same, it means that the terms in the expression have different values. In such cases, you cannot directly combine or simplify the terms using the exponent rules.
Let's consider an example: If you have the expression 3^4 + 2^3, the base of the first term is 3, and the base of the second term is 2. Since the bases are different (3 and 2) and the exponents are also different (4 and 3), you cannot simplify this expression directly using exponent rules.
To evaluate or simplify such expressions, you would need to calculate the values of each term separately and then combine them. In this case, you would compute 3^4 (= 81) and 2^3 (= 8) individually, and then add the results together: 81 + 8 = 89.
So, when the bases are not the same or the exponents are not the same, you cannot directly combine terms using exponent rules. You need to calculate each term separately and then perform any further calculations as needed.