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

Use rational exponents to write as a single radical expression. Assume that all variables represent positive real numbers
5√5 *3√x

5√(5)3√(x)

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.

51/5x1/3

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.

53/15x5/15

Now we can switch back to radical notation

15√(53)15√(x5)

With the same type of root we can multiply these

15 √(53x5)

And further simplifying the term 53 gives the answer

15√(125x5)
Rewrite the radicals as fractional exponents then find a common denominator

(51/5)(x1/3)=(53/15)(x5/15)=(53x5)1/15=15√(53x5)