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Rational Exponents and Radicals

Rational Exponents and Radicals 1.4 - Solution

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To simplify the given expression, remember that the numerator of a rational exponent is the exponent of the expression, and the denominator is the index. a1n=an and amn=amn\begin{gathered} a^\frac{1}{{\color{#009600}{n}}}=\sqrt[{\color{#009600}{n}}]{a} \quad \text{ and } \quad a^\frac{{\color{#FF0000}{m}}}{{\color{#009600}{n}}}=\sqrt[{\color{#009600}{n}}]{a^{\color{#FF0000}{m}}} \end{gathered} Let's simplify the expression!
(x3)52\left(x^3\right)^\frac{5}{2}
(x3)512\left(x^3\right)^{5\cdot \frac{1}{2}}
((x3)5)12\left(\left(x^3\right)^5 \right)^\frac{1}{2}
(x35)12\left(x^{3\cdot5}\right)^{\frac{1}{2}}
(x15)12\left(x^{15}\right)^{\frac{1}{2}}
a12=aa^{\frac{1}{2}}=\sqrt{a}
x15\sqrt{x^{15}}