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

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

The area is what?

(Type a simplified exponential expression.)

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2 Answers

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 3x* 8x4 = 3*x*x*x*8*x*x*x*x = 24x7.  

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

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