I'm probably letting the layout of this problem confuse me but I need help. I need to multiply and express in simplest form: (x-5/2)^3*(1/x-5)^2
If you mean
[(x-5)/2]^3*[1/(x-5)]^2 , then the simplest-form answer is
(1/8)(x-5)^3
write 14 days to 7days as a ratio in simplest form
To multiply and express in simplest form, we can follow these steps:
Step 1: Simplify each term separately.
Let's start by simplifying the first term, (x-5/2)^3, using the exponent rule for exponents of powers:
(x-5/2)^3 = x^3 - (3 * x^2 * 5/2) + (3 * x * (5/2)^2) - ((5/2)^3)
Expanding this expression further, we get:
x^3 - (15/2) * x^2 + (75/4) * x - (125/8)
Now, let's simplify the second term, (1/x-5)^2:
(1/(x-5))^2 = 1^2 / (x-5)^2 = 1 / (x-5)^2
We have simplified both terms. Now, let's multiply the two expressions together:
Step 2: Multiply the expressions.
(x^3 - (15/2) * x^2 + (75/4) * x - (125/8)) * (1 / (x-5)^2)
To simplify this, we can multiply the numerators and denominators separately, and then combine them.
(x^3 * 1) - ((15/2) * x^2 * 1) + ((75/4) * x * 1) - ((125/8) * 1) / (x-5)^2
Combining the terms, we get:
x^3 - (15/2) * x^2 + (75/4) * x - (125/8) / (x-5)^2
This is the expression multiplied and expressed in its simplest form.
If you need to simplify further, you can check if there are any common factors in the numerator and denominator and cancel them out. However, without additional context or constraints, we cannot simplify it any further.