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Simplify the following expression. Express your answer as a single radical.

Simplify the following expression. Express your answer as a single radical.-example-1

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We can rewrite radicals as fractional exponents, like the following example


\sqrt[y]{x}=x^{(1)/(y)}

Using this rule in our problem, we can rewrite our expression as


\sqrt[4]{5}\sqrt[16]{5}=5^{(1)/(4)}\cdot5^{(1)/(16)}

When we have a product of two exponentials with the same basis, we just add the exponents.


a^b\cdot a^c=a^(b+c)

Using this property in our problem, we have


5^{(1)/(4)}\cdot5^{(1)/(16)}=5^{(1)/(4)+(1)/(16)}=5^{(4)/(16)+(1)/(16)}=5^{(5)/(16)}=\sqrt[16]{5^5}=\sqrt[16]{3125}

And this is our result.


\sqrt[4]{5}\sqrt[16]{5}=\sqrt[16]{3125}

User Eduard Sukharev
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