Question

The area of a rectangle is 54x^9 y^8 square yards. If the length of the rectangle is 6x^3 y^4 which expression represents the width of the rectangle in yards?

Jack knows a=l*w, so he writes the following equation:
54x^9 y^8= 6x^3 y^4*w
He divides both sides by the length:
(54x^9 y^8)/(6x^3 y^4 )=9 x^12 y^12


Error:

Correct solution:

Answer 1

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➷ Error: When he divided both sides by the length, he didn't subtract the exponents. Instead on subtracting the exponents, he added them - which is incorrect.

Correct solution: 54x^9 y^8 / 6x^3 y^4 = 9x^6 y^4

The width is 9x^6 y^4

(This is based on the rule that when you divide values with exponents, you have to subtract the exponents)

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Answer 2

Error: He added the exponents of the variables. The exponents must be subtracted.

Correct solution:
`w=9x^6y^4`

Explanation:

According the quotient property of exponents, when you divide two powers with equal base, you must subtract the exponents.

Therefore, keeping the property above on mind, you have:

`w=(54x^9y^8)/(6x^3 y^4)\\\\w=9x^((9-3))y^((8-4))`

Therefore, you have that the width of the rectangle is the shown below:

`w=9x^6y^4`