Question

If a²b³=32/27​ and a/b³​=27/4​, what is the value of ab?

Answer 1

After solving the given equations for 'a' and 'b', we find that the value of 'ab' is 4/3.

Step-by-step explanation:

To solve the question If a²b³=32/27 and a/b³=27/4, what is the value of ab?, we can manipulate the given equations to find the values for 'a' and 'b' and then determine 'ab'.

First, let's express both equations in terms of 'a':

1. a²b³ = 32/27 (1)

2. a/b³ = 27/4 (2)

From equation (2), we can solve for 'a' directly: a = 27b³/4.

Now, substitute this expression for 'a' into equation (1):

(27b³/4)² * b³ = 32/27. After simplifying, we see that b¹⁵ = (32/27) * (16/729) b¹⁵ = 512/19683.

Now we can find the value of 'b' by taking the 15th root: b = √[ⁱ⁵]{512/19683} This simplification gives us b = 2/3.

Using the value of 'b', we can go back to equation (2) and find 'a': a = 27*(2/3)³/4 a = 27*(8/27)/4 a = 8/4 a = 2.

Finally, we calculate the value of 'ab': ab = 2 * 2/3 ab = 4/3.

Therefore, the value of 'ab' is 4/3.