SAT® Math Question

[Katty2010]

Caution:- I am very very dumb at math!

Please help me with couple of question & let me know the method of solving:-

Q1- If a (exponent or is to power) b a^b=4, and 3b=2, what is the value of a?
_________________
Just a confused kid... trying to live through twists & turns of life!
------
Everything Is Temporary!

[Satkiddo]

since b = (2/3), we can rewrite a^b and change that into a^(2/3).

Now:

a^(2/3) = 4

the trick for all exponent problems is that you have to get all the numbers into prime bases. so we turn that 4, into 2^2:

a^(2/3) = 2^2

We can then take both sides to the (3/2) power (so that the 2/3 cancels out):

[a^(2/3)]^(3/2) = [2^2]^(3/2)
You will now see that:

a = 2^3 = 8