Question

(root 8)^a = 4^b/3

If a and b are positive numbers in the equation
above, then what is the value of a/b ?

A. 4/9
B. 2/3
C. 3/2
D. 9/4

Answer 1

4/9

Step-by-step explanation:

√8^a=4^b/3.

You can rewrite √8^a as 8^a/2.

So then that would be, 8^a/2=4^b/3.

If both sides have the same base, we could then make the fractional exponents equal to each other. Since 2^3=8 and 2^2=4, we can make that possible.

2^3(a/2)=2^2(b/3).

2^3a/2=2^2b/3.

So now 3a/2=2b/3.

Then we isolate the a, by multiplying 2/3 on both sides and are left with:

a=2/3*2/3*b

a=4/9*b

Then you divide both sides by b to get:

a/b=4/9.