What is the area of a rectangle if one side has a length of #12x^3# and the other side has a width of #6x^2#?

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Answer 1 · 2017-01-03T22:07:56

The area of the rectangle is #72x^5#

The formula for the area of a rectangle is:

#A = l xx w#

Where,

#A# is the area, what we are solving for in this problem.

#l# is the length which has been given as #12x^3#

#w# is the width which has been given as #6x^2#

Substituting these values gives:

#A = 12x^3 xx 6x^2#

Simplifying gives:

#A = (12 xx 6) xx (x^3 xx x^2)#

We can multiply the constants and use the rule for exponents to multiply the #x# terms.

#y^color(red)(a) xx y^color(blue)(b) = y^(color(red)(a)+color(blue)(b))#

This gives:

#A = 72 xx (x^(3+2))#

#A = 72 xx x^5#

#A = 72x^5#