Write an explanation of why (x^3)(x^4) is not x^12.?

Question

can anyone give me a good explanation. I am finding it hard to explain.

Answer 1

x^3 means three x-s multiplied together.
x^4 means four x-s multiplied together.
When you multiply the two results, you get seven x-s multiplied together.
If the answer were to be x^12, you would need to find another five x-s from somewhere, and you don't have them.

Answer 2

Because in the multiplication of values the resulting exponents are the sum and not the product.

In this case exponent 3 + exponent 4 = exponent 7 therefore the product of x^3 and x^4 = x^7 rather than x^12.

Answer 3

X^3 means X multiplied by itself 3 times.X x X x X
X^4 means X multiplied by itself 4 times.X x X x X x X
x^3(x^4) means (X x X x X x X x X x X x X) .
The above three staements prove that (x^7)

Answer 4

Example
a² x a³ = (a x a) x (a x a x a) = a^5
The example would suggest that when multiplying, the indices are ADDED.
Thus (x^3) X (x^4) = x^7

Answer 5

Because when you multiply with exponents you add the exponential number. it is the same theory when you divide them , then you subtract exponents so x^3*x^4= x^3=4=x^7

Answer 6

because
x^3 = x.x.x AND
x^4 = x.x.x.x
so (x^3)(x^4)= x.x.x.x.x.x.x=x^7

Answer 7

(a^n)(a^m) = a^(n+m)
(x^3)(x^4)=x^7
but:
(x^n)^m=x^(n*m)