Simplify (6x^-2) (0.5x)^4

(3/8)x^2

Step-by-step explanation:

Rewriting the given expression as follows simplifies the solution.  Note that 6x^(-2) could be written as:

   6

 x^2

Also, (0.5x)^4 = 0.0625x^4.

Then we have:

6*0.0625*x^4        0.375

= * x^(4-2), or     (3/8)x^2

        x^2                     1

Note that x^4 / x^2 = x^2.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)