The area of a rectangle is 81x^10y^2. if the length of the rectangle is 3x^6y^-4, find the width

width = (27x⁴)(10y⁶)

Step-by-step explanation:

Multiplying numbers will multiply their coefficient. For 3x, 3 must multiply with another number to get 81. That number is 27, so 3x(27) = (3⋅27)x = 81x.

Now you need the power.

Multiplying numbers with the same base will add up their exponent. I got x⁶ but need to get to x¹⁰.

Just multiply it by x⁴ so that you get (x⁶)(x⁴) = x⁶⁺⁴ = x¹⁰.

Do the same for y.

A = LW

(81x¹⁰)(10y²) = (3x⁶)(y⁻⁴)(W)

(81x¹⁰)(10y²) = (3x⁶)(y⁻⁴)(27x⁴)(10y⁶)

(81x¹⁰)(10y²) = (3x⁶)(27x⁴)(y⁻⁴)(10y⁶)

(81x¹⁰)(10y²) = (3⋅27x⁶⁺⁴)(y⋅10⁻⁴⁺⁶)

(81x¹⁰)(10y²) = (81x¹⁰)(10y²)

width = (27x⁴)(10y⁶)