Which of the following is the rational exponent expression of ^3 to the square root of 4n? a. (4n)^3 b. 3n^4 c. (4n)^1/3 d. 4n^1/3

The root index becomes the denominator of the rational fraction power. The appropriate choice is

... C. (4n)^(1/3)

The Order of Operations requires you evaluate (4n)^1/3 as ((4n)^1)/3 = (4/3)n. That is not what you intend. Parentheses are required around any exponent that contains any kind of arithmetic operation.

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week