Explain rational exponents as extensions of integer exponent rules and as radical notation.
Rewrite a radical as a rational exponent by matching the root index to the denominator
Problem
Rewrite \(\sqrt{x^{3}}\) as \(\text{one}~\text{power}\) of \(x\). Put the inner exponent in the numerator and the square-root index in the denominator.
Big Picture
What this problem is really about
To convert a radical to one power, the inner exponent becomes the numerator and the root index becomes the denominator. We’ll rewrite the radical as a fractional power, multiply the nested exponents, and map the resulting fraction back to confirm the original radical.
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