Question 1:

x <- 1.1
a <- 2.2 
b <- 3.3  

#a.
z <- x^(a^b)

#b.
z <- (x^a)^b

#c.
z <- 3*x^3 + 2*x^2 + 1

Question 2:

#a.
vecA <-  c(seq(1, 8), rev(seq(1, 7)))

#b.
vecB <- rep(1:5, times = 1:5)

#c.
vecC <-  c(rep(5, 1), rep(4, 2), rep(3, 3), rep(2, 4), rep(1, 5))

Question 3:

x <- runif(1)
y <- runif(1)
yx <- y/x

r <- sqrt(x^2 + y^2) 
theta <- atan(yx)

Question 4:

queue <- c("sheep", "fox", "owl", "ant")

#a.
queue[5] = "serpent"

#b.
queue <- queue[-c(1)]

#c.
queue <- c("donkey", queue)

#d.
queue <- queue[-c(5)]

#e.
queue <- queue[-c(3)]

#f.
queue <- c(queue[1:2], "aphid", queue[3])

#g.
which(queue == "aphid")
## [1] 3

Question 5:

numbers <- c(1:100)

# Filter numbers that are not divisible by 2, 3, or 7
filtered_numbers <- numbers[!(numbers %% 2 == 0 | numbers %% 3 == 0 | numbers %% 7 == 0)]