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College
Calculus and Analysis
Integral Calculus
Rational exponents and radicals

Dolly Robinson

Answered question

2020-11-26

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.

\sqrt{x^{3}}

Answer & Explanation

averes8

Skilled2020-11-27Added 92 answers

Concept used:
If a is real number n is a positive integer and $\sqrt[n]{a^{m}} is a real number then the rational exponent expression \sqrt[n]{a^{m}} is equivalent to radical expression a^{\frac{m}{n}} .$
The above statement can be express as,
$\sqrt[n]{a^{m}} = a^{m / n}$
Calculation:
The given expression is $\sqrt{x^{3}} .$
The property of nth $\sqrt{}$ is,
$\sqrt[n]{a^{m}} = a^{m / n}$
Substitute 2 for n, 3 for m and x for a in the above equation.
$\sqrt[2]{x^{3}} = {(x^{1 / 2})}^{3}$
$= x^{3 / 2}$
Hence, the solution of the expression $\sqrt{x^{3}} i s x^{3 / 2}$

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

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