Explanation

8^𝑎 = 16^𝑏

We can rewrite 16 as 2^4, so:

(2^3)^𝑎 = (2^4)^𝑏

Using the power rule (a^m)^n = a^(mn), we get:

2^(3𝑎) = 2^(4𝑏)

Since the bases are equal (both are 2), we can equate the exponents:

3𝑎 = 4𝑏

Now, divide both sides by 3𝑏:

𝑎/𝑏 = 4/3

So, the ratio of 𝑎 to 𝑏 is 4:3 or 4/3.