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

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2 Answers

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)