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Rewrite in simplest radical form square root of x times the fourth root of x. Show each step of your process.
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[tex]\sqrt[4] {x^3}[/tex]

Step-by-step explanation:

At this point, we can transform the square root into a fourth root by squaring the argument, and bring into the other root:

[tex]\sqrt x \cdot \sqrt[4] x =\sqrt [4] {x^2} \cdot \sqrt[4] x = \sqrt[4]{x^2\cdot x} = \sqrt[4] {x^3}[/tex]

Alternatively, if you're allowed to use rational exponents, we can convert everything:

[tex]\sqrt x \cdot \sqrt[4] x = x^{\frac12} \cdot x^\frac14 = x^{\frac12 +\frac14}= x^{\frac24 +\frac14}= x^\frac34 = \sqrt[4] {x^3}[/tex]
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