The area of a rectangle is 48x^8y^9 square yards. if the length of a rectangle is 8x^4y^3 which?

Question

...  expression represents the width of the rectangle in yards ? 

A) 6x^4y^3
B) 40x^4y^6
C) 6x^4y^6
D) 56x^12y^12

Answer

(48x^8) (y^9) = (8x^4) (y^3) (ax^n by^m)

This is not hard, it's just a profusion of values. We can break it into four equations, one for x values and one for y values, and two for the coefficients.

48 = 8 . 6 (using . instead of x to multiply) so a = 6

The y coefficient does not change. (b=1)

x^8 = x^4 . x^2 so n = 2

y^9 = y^3 . y^3 so m = 3

Putting it all together we have 6x^2 y^3 and there is no correct answer. 

This is a good demonstration of the importance of correct presentation and addition of spaces to improve readability.

Answer

As
x^n * x^m = x^(n+m)

answer C) is correct:

8x^4 * y^3 * 6x^4 * y^6 = (8 * 6)x^(4+4) * y^(3+6) =

48x^8 * y^9

The area of a rectangle is 48x^8y^9 square yards. if the length of a rectangle is 8x^4y^3 which?

Answers (2)