By which factor does b increase if a is multiplied with 2?

Question

Consider $$2a^2 = 3b^3.$$

By which factor does b increase if a is multiplied by 2?

Answer is 4. Can anyone explain it to me?

Answer 1

Initially, $b=b_0=\frac{2}{3}a^{2/3}$. If $a \to 2a$ then $3b^3=2(2a)^2=4 \cdot 2a^2 \implies b=4^{1/3} \cdot b_0$. So the answer it's not exactly 4 but $4^{1/3}$.

Answer 2

$$2a^2=3b^3$$ $$2(2a)^2 = 3(kb)^3$$ Solve for $k$.