A and b are positive integers and a–b = 3. Evaluate the following:
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a) (9^(0.5b))/3a
b) (27^(1/3b)) /(9^(0.5b))
c) ( 125^(1/3a))/(25^(1/2b))

a) 1/27

b) 1

c) 125

Step-by-step explanation:

a) (9^(0.5b))/(3^a)

(3²)^(0.5b) ÷ (3^a)

(3^b) ÷ (3^a)

3^(b - a)

a - b = 3

b - a = -3

3^(-3)

1/27

b) (27^(1/3b)) /(9^(0.5b))

(3³)^(b/3) ÷ (3²)^(0.5b)

(3^b) ÷ (3^b)

1

c) ( 125^(1/3a))/(25^(1/2b))

(5³)^(a/3) ÷ (5²)^(b/2)

5^a ÷ 5^b

5^(a - b)

5³

125

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.