Subjects algebra

Fractional Exponent 873C15

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Question: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). $3^{8/5}$ The expression above can also be written in the form $\sqrt[5]{a^b}$. For this expression, $a = [ ]$, $b = [ ]$, and $c = [ ]$.
1. **State the problem:** We are given the expression $$3^{8/5}$$ and asked to rewrite it in the form $$\sqrt[5]{a^b}$$, where $$a$$ and $$b$$ are numbers to find. 2. **Recall the rule for fractional exponents:** $$x^{m/n} = \sqrt[n]{x^m}$$ This means that $$3^{8/5} = \sqrt[5]{3^8}$$. 3. **Identify the values:** Here, $$a = 3$$ and $$b = 8$$. 4. **About $$c$$:** The problem mentions $$c$$ but the expression $$3^{8/5}$$ rewritten as $$\sqrt[5]{3^8}$$ only involves $$a$$ and $$b$$. If $$c$$ refers to the root index, then $$c = 5$$. **Final answers:** $$a = 3$$ $$b = 8$$ $$c = 5$$