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Which expression is equivalent to this equation?

 May 22, 2017
 #1
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The answer is "C", x^(1/3).

 May 22, 2017
 #2
avatar+2340 
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C; \(\sqrt[3]{x}\)

 

Why? Well, here we go. Let's start with the original:

 

\(\frac{\sqrt[3]{x^2}}{\sqrt[6]{x^2}}\)  Change both of these square roots to exponents

\(\frac{x^{\frac{2}{3}}}{x^{\frac{2}{6}}}\)

 

Now let's apply an exponent rule. The rule is the following. 

\(\frac{x^a}{x^b}=x^{a-b}\)

 

Using this rule, we can simplify further:

 

\(\frac{x^{\frac{2}{3}}}{x^{\frac{2}{6}}}=x^{\frac{2}{3}-\frac{1}{3}}\) I simplified 2/6 to 1/3. Now, subtract the exponents.

 

\(x^{\frac{1}{3}}=\sqrt[3]{x}\)This is your final answer. Hopefully, this makes sense...

 May 22, 2017

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