How is this possible? Can someone explain?

Question

My teacher says that $W^{2/7}B^{5/7}=1$ is equivalent to $W^2B^5=1$. Can someone explain this rule to me? Am I always able to just take the variable and raise it to the numerator of the fractional exponent?

Answer 1

If $$W^{2/7} \times B^{5/7} = 1$$

then by raising each side to the seventh power, we get

$$1 = 1^7 = (W^{2/7} \times B^{5/7})^7 = (W^{2/7})^7 \times (B^{5/7})^7 = W^2 B^5$$

We have used the facts that

$$(a^b)^c = a^{bc} \text{ and } (ab)^c = a^c b^c$$