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?
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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
$$(a^b)^c = a^{bc} \text{ and } (ab)^c = a^c b^c$$
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1Wow. That's one to slap your forehead on. Can't believe I was so confused on that one. Thanks so much for clearing it up!! – briteId Sep 12 '13 at 03:00
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Why the downvote? – Sep 12 '13 at 03:12