Fractional exponents follow the same laws as integer exponents: CK-12 Foundation
Consider the function $f(x) = x^1/2$. This function represents the square root of $x$. The graph of $f(x)$ is a curve that increases as $x$ increases. Fractional Exponents Revisited Common Core Algebra Ii
bm/n=bmn=(bn)mb raised to the m / n power equals the n-th root of b to the m-th power end-root equals open paren the n-th root of b end-root close paren to the m-th power Fractional exponents follow the same laws as integer
$9^\frac32 = (3)^3 = 27$.
For real numbers and even roots, $(a^m)^\frac1n = a^\fracmn$ holds only if we ensure the result yields a non-negative value for the principal root. Thus: $$ (x^2)^\frac12 = |x|$$ And more generally, for even $n$: $$ (x^n)^\frac1n = |x|$$ Fractional Exponents Revisited Common Core Algebra Ii