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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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Aaron R. | Experienced Tutor, Master's in Physics, Bachelor's in Physics, MathExperienced Tutor, Master's in Physics, ...
5.0 5.0 (90 lesson ratings) (90)

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.  

Luke B. | fun + learning = inevitable progressfun + learning = inevitable progress
4.9 4.9 (90 lesson ratings) (90)

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

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