EXPS 1 | Lesson 4 | Try This! (Matching)

Try This! Matching

In Explore (Doubling), the relationship between fractional exponents and radicals was developed for exponential expressions in base two. 

In general, the relationship between any fractional exponent and its base can be translated to a radical expression (and visa versa) as shown below:

\(x^\frac{1}{2}=\sqrt{x}\); and \(x^\frac{1}{3}=\sqrt[3]{x}\); and in general \(x^\frac{1}{r}=\sqrt[r]{x}\)
\(x^\frac{p}{r}=\sqrt[r]{x^p}\) or \(\big(\sqrt[r]{x}\big)^p\) where \(p\) is the power and \(r\) is the root. 

Using these general rules, match each radical expression to an exponential expression in the table below.

1. \(\sqrt[3]{2^2}\)a. \(3^{\frac34}\)
2. \(\sqrt[4]{3^2}\)b. \(625^{\frac13}\)
3. \(\sqrt[]{5^3}\)c. \(16^{\frac14}\)
4. \(\sqrt[3]{625}\)d. \(5^{\frac32}\)
5. \(\sqrt[4]{16}\)e. \(4^{\frac14}\)
6. \(\sqrt[4]{4}\)f. \(2^{\frac23}\)
7. \(\sqrt[4]{27}\)g. \(3^{\frac12}\)

Solutions : 1=f, 2=g, 3=d, 4=b, 5=c, 6=e, 7=a

Go to Watch (Roots as Exponents)

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