^{5}√5 *

^{3}√x

Use rational exponents to write as a single radical expression. Assume that all variables represent positive real numbers

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To write this expression as a single radical, we must find a way to express the terms with the same type of root so that we may multiply them together. First, we rewrite the terms with fractional exponents.

5^{1/5}x^{1/3}

Given that the denominator represents the type of root, we can multiply the terms by finding the lowest common denominator of their exponents. For 3 and 5 this is 15, so we rewrite both of our terms with exponents that have a denominator of 15.

5^{3/15}x^{5/15}

Now we can switch back to radical notation

With the same type of root we can multiply these

And further simplifying the term 5^{3 }gives the answer

Ryan S. | Mathematics and StatisticsMathematics and Statistics

Rewrite the radicals as fractional exponents then find a common denominator

(5^{1/5})(x^{1/3})=(5^{3/15})(x^{5/15})=(5^{3}x^{5})^{1/15}=^{15}√(5^{3}x^{5})

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