please write an explaination why (x^3)(x^4) is not x^12. I am confused thank you.

it is not the answer because, first of all, try replacing x with another number, in this case, let's say two.
(2^3)(2^4)= 128, and if you try 2^12, you do not get 128, instead your answer would be 4,096. The same with any other number. so try finding the number that would fit in. I found (2^7)=128.
so now try another number, 4.
(4^3)(4^4)= 16,384 let's check that. 4^7= 16384. so it wouldn't be x=12, it would be x=7. try replacing a variable with different numbers.

To explain why (x^3)(x^4) is not equal to x^12, let's break down the problem by understanding how exponents work.

When you have an expression like (x^3)(x^4), it means you are multiplying two terms with the same base, x, and raising each term to a different exponent, 3 and 4, respectively. To simplify this expression, you can add the exponents. So combining the exponents gives you x^(3+4), which becomes x^7.

To verify if this is the correct answer, we can substitute different values for x and see if the expression holds true.

For example, let's try substituting x with 2:
(2^3)(2^4) = 8 * 16 = 128

Now, let's try substituting x with 2 in the expression x^12:
2^12 = 4096

As you can see, 128 (the value obtained from (2^3)(2^4)) is not equal to 4096 (the value obtained from 2^12). This indicates that x^12 is not the correct answer for (x^3)(x^4).

By substituting different values for x and performing these calculations, you can verify that x^7 is the correct solution.