Which property of exponents must be used first to solve this expression? (xy^2)1/3

I think you meant (xy^2)^(1/3), where 1/3 is the exponent of (xy^2).

Normally you must perform any operations showin inside parentheses first. But here xy^2 cannot be simplified. Your first step, then, is to apply the exponent (1/3) to (xy^2). Note that you're not "solving" this expression; rather, you're "evaluating it."

(xy^2)^(1/3) comes out to x^(1/3)*y^(2/3). This expression cannot be simplified further.

answer: im gonna go with milli

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt