SOLUTION: How do you multiply {{{ x^5x^7 }}}

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Question 70331This question is from textbook Algebra 2
: How do you multiply +x%5E5x%5E7+ This question is from textbook Algebra 2

Found 2 solutions by josmiceli, bucky:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E5x%5E7+
This is the same as
%28x%2Ax%2Ax%2Ax%2Ax%29%2A%28x%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%29
which is just
%28x%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%29
or x%5E%285%2B7%29+=+x%5E12

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
You multiply %28x%5E5%29%2A%28x%5E7%29 by just adding the two exponents to get x%5E12.
.
Think about it. By the definition of exponents:
.
x%5E5+=+x%2Ax%2Ax%2Ax%2Ax and
x%5E7+=+x%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax
.
When you multiply the right sides of these two equations the problem becomes:
.
%28x%2Ax%2Ax%2Ax%2Ax%29%2A%28x%2Ax%2Ax%2Ax%2Ax%2Ax%2Ax%29
.
so you end up with 12 x's all multiplied together which is, by definition, x%5E12
Hope this helps you understand why the exponent is 12.