CPhill

I assume the "3 + 1/2" is an interest rate of 3.5% = .035 in decimal form

So we have

£8000(1+ .035)⁵ = about £9501.5

(5^2)^-3/5^-8    so we have

(5²)^-3/ 5^-8   and by a law of exponents, we can write

5^-6 / 5^-8      and again, by an exponent law, we have

5⁸ / 5⁶ = 5^8-6 = 5² =  25

(x14)/(x7) = (14x)/(7x) = 2      (with the restriction that x ≠ 0)

180/365  is about the same as 180/360 = about 1/2 of a year

Multiplication

10 sec * 20ft/sec = 200 ft

If we consider that the pyramid has a solid "bottom"...the area of this "bottom" =  7.2² = 51.84 sq units

And subtracting this from 256.7 gives the total area of the sides = 204.86 sq units. And the area of each side is 1/4 of this = 51.215 sq units

And since each side is a triangle with a base of 7.2, we have

51.215 = (1/2)*7.2* h    

51.215 = 3.6 * h      divide both sides by 3.6

h = about 14.23 units = the slant height

8251 = 1.27N     divide both sides by 1.27

8251/ 1.27  = about 6496.85 

3√27 = 3ⁿ

3√(9*3) = 3ⁿ

9√3 = 3ⁿ      write the left side in terms of exponents using the base of 3

(3)² * 3^1/2 = 3ⁿ

(3)^5/2 = 3ⁿ

So n = 5/2

We can always find this by taking the ratio of the logs of both numbers....so we have

log(256) / log(4)= 4

Nice LaTex presentation, DS  .....!!!