
Aaron R. answered 04/09/13
Experienced Tutor, Master's in Physics, Bachelor's in Physics, Math
This question is about how to handle exponents in terms that are multiplied together. As a general rule, if you have an expression like xa * xb you can simplify this to xa+b. In order to demonstrate, let's let a = 2, and b = 3. In this case we want x2 * x3. If we remember what the exponents mean, we can re-write this as x*x*x*x*x because from the first term we have 2 x's and from the second term we have 3 x's. Well we can write this with an exponent as well: x*x*x*x*x = x5. But this also equals x2+3. So we've demonstrated that x2 * x3 = x2+3 = x5.
Once again, to put this generally, we have xa * xb = xa+b.
Applying this to the problem, we have 3x3 * 8x4 = 3*x*x*x*8*x*x*x*x = 24x7.