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)