27p^3-1/216-9/2p^2+1/4p solve the problem
solve? Where is an equal sign?
well, it's the same as
(18p-1)^3 / 216
To solve the problem, we need to simplify the given expression. Let's break down each term and simplify them one by one:
Term 1: 27p^3
This is already in its simplest form, so we can leave it as is.
Term 2: -1/216
We can simplify this fraction by taking 1 as the numerator and 216 as the denominator. Since 216 is a multiple of 6, we can simplify further:
1 ÷ 216 = 1/216.
Therefore, Term 2 becomes -1/216.
Term 3: -9/2p^2
This term includes a variable, p, in the denominator. To simplify this expression, we can factorize -9/2 into two separate fractions:
-9/2p^2 = (-9/2) * (1/p^2).
Next, we can simplify the fraction -9/2 by multiplying both the numerator and the denominator by 2, which changes the fraction to -18/4:
(-18/4) * (1/p^2).
Now we will rewrite the expression as:
-18/4 * 1/p^2 = -18/(4p^2).
Term 4: 1/4p
This term is already in its simplest form, so we can leave it as is.
Now, let's put all the terms together:
27p^3 - 1/216 - 9/(4p^2) + 1/(4p).
To combine the terms, we need a common denominator. The simplest common denominator is 216p^2. We can rewrite each term with the common denominator:
(27p^3 * 216p^2)/(216p^2) - (1 * p^2 * 216)/(1 * 216p^2) - (9 * 54)/(4 * 54p^2) + (p * 54)/(p * 54p).
After simplifying, we get:
5832p^5/216p^2 - 216p^2/216p^2 - 486/216p^2 + 54/54p^2.
Now, let's combine like terms:
5832p^5 - 216p^2 - 486 + 54/54p^2.
Finally, we can simplify further by rearranging the terms:
5832p^5 - 216p^2 - 486 + 1/p^2.
Therefore, the simplified expression is:
5832p^5 - 216p^2 - 486 + 1/p^2.