What solves the p equation p to the -5th power = 1/243

p = 3

Step-by-step explanation:

Symbolically, your math problem reads:

  1            1

=

 p^5       243

We need only solve p^5 = 243 to obtain p.

Note that p^5 = 243.  

You're not really expected to memorize 5th powers (tho' it's nice if you can).

Instead, factor 243; we get 3(81), or 3(3)(27).  Note that 3(3)(27) = 3(3^1)(3^3).  Identify and add together all the exponents of p here:  1+1+3 = 5.  This tells us that 243 = 3^5.

Thus, p^5 = 243, and p = 3.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)