factor down (4^3)^2
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when is it not possible to work an exponent multipication?
In the space below give an example and work it out to prove what you say does not work
(4^3)^2 = 4^6 = 4^3 * 4^3 = 4 * 4 * 4 * 4 * 4 * 4 = 4,096
I don't know when it is not possible.
To simplify the expression (4^3)^2, we need to understand the properties of exponents.
When we have a number raised to a power raised to another power, we can simplify by multiplying the exponents. In this case, we raise 4 to the 3rd power, which gives us 4^3. Then, we raise the result to the power of 2, giving us (4^3)^2.
To simplify further, we multiply the exponents: 3 * 2 = 6. So, (4^3)^2 simplifies to 4^6.
Now, let's move on to the second part of your question. There is no such thing as "exponent multiplication" as you mentioned. However, there is a concept called "exponentiation," which refers to raising a number to a power.
It is always possible to work with exponentiation. However, there are cases where simplification is not possible because the numbers involved are not simplified themselves. For example:
2^(3 + 2) cannot be further simplified because 3 + 2 equals 5, and there are no common factors or other properties that allow us to simplify it.
To illustrate this, let's work it out:
2^(3 + 2) can be rewritten as 2^5, where 3 + 2 equals 5.
Now, let's try to simplify it further. We cannot factor 2^5 any more because 2 is a prime number, and there are no common factors. Therefore, we stop at 2^5.
In short, while working with exponents, always look for simplification opportunities by applying the appropriate properties. However, not all expressions can be further simplified based on the numbers involved.