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 x^{a} * x^{b} you can simplify this to x^{a+b}. In order to demonstrate, let's let a = 2, and b = 3. In this case we want x^{2} * x^{3}. 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 = x^{5}. But this also equals x^{2+3}. So we've demonstrated that x^{2} * x^{3} = x^{2+3} = x^{5}.

Once again, to put this generally, we have x^{a} * x^{b} = x^{a+b}.

Applying this to the problem, we have 3x^{3 }* 8x^{4} = 3*x*x*x*8*x*x*x*x = 24x^{7}.