Answer:
[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]
Step-by-step explanation:
A radical represents a fractional power. For example, ...
[tex]\sqrt{x}=x^{\frac{1}{2}}[/tex]
This makes sense in view of the rules of exponents for multiplication.
[tex]a^ba^c=a^{b+c}\\\\a^{\frac{1}{2}}a^{\frac{1}{2}}=a^{\frac{1}{2}+\frac{1}{2}}=a\\\\(\sqrt{a})(\sqrt{a})=a[/tex]
So, a root other than a square root can be similarly represented by a fractional exponent.
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The power of a radical and the radical of a power are the same thing. That is, it doesn't matter whether the power is outside or inside the radical.
[tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}=(\sqrt[n]{x})^m[/tex]
