Answer:
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
The value of (9^(0.5b))/3a when it is evaluated is 1/27.
The value of (27^(1/3b)) /(9^(0.5b)) when it is evaluated is 1.
The value of ( 125^(1/3a))/(25^(1/2b)) when it is evaluated is 125.
(9^(0.5b))/3a
Simplify 9 as the square of 3.
= (3²^(0.5b)) / 3a
= (3²^(1/2b)) / 3a
Multiply the powers 2 and 1/2 together
= 3^b / 3a
= 3^(b - a)
a - b = 3
b - a = -3
[tex]3^{-3}[/tex] = 1/27
(27^(1/3b)) /(9^(0.5b))
(3³^(1/3b)) / (3²^(0.5b)
3^b / 3^b
= 1
( 125^(1/3a))/(25^(1/2b))
(5³^(1/3a)) / (5²^(1/2b))
5^a / 5b
5^(a - b)
5^3 = 125
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