Using the formula A=lw, find the area of the rectangle.

Question

The measurements given are 3x^3 and 8x^4

The area is what?

(Type a simplified exponential expression.)

Answer 1

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 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 x^a * x^b = x^a+b.  

Applying this to the problem, we have 3x³ * 8x⁴ = 3*x*x*x*8*x*x*x*x = 24x⁷.  

Answer 2

One is the length and one is the width, so multiply them!

3x^3 * 8x^4 = (24x^3)(x^4) = 24x^7