Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. displaystylesqrt{{{x}^{3}}}

Question
Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
$$\displaystyle\sqrt{{{x}^{3}}}$$

2020-11-27
Concept used:
If a is real number n is a positive integer and $$\displaystyle{\sqrt[{{n}}]{{{a}^{m}}}}\ \text{is a real number then the rational exponent expression}\ \displaystyle{\sqrt[{{n}}]{{{a}^{m}}}}\ \text{is equivalent to radical expression}\ \displaystyle{a}^{{\frac{m}{{n}}}}.$$
The above statement can be express as,
$$\displaystyle{\sqrt[{{n}}]{{{a}^{m}}}}={a}^{{{m}\text{/}{n}}}$$
Calculation:
The given expression is $$\displaystyle\sqrt{{{x}^{3}}}.$$
The property of nth $$\displaystyle{\sqrt[]{}}$$ is,
$$\displaystyle{\sqrt[{{n}}]{{{a}^{m}}}}={a}^{{{m}\text{/}{n}}}$$
Substitute 2 for n, 3 for m and x for a in the above equation.
$$\displaystyle{\sqrt[{{2}}]{{{x}^{3}}}}={\left({x}^{{{1}\text{/}{2}}}\right)}^{3}$$
$$\displaystyle={x}^{{{3}\text{/}{2}}}$$
Hence, the solution of the expression $$\displaystyle\sqrt{{{x}^{3}}}{i}{s}{x}^{{{3}\text{/}{2}}}$$

Relevant Questions

Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
$$\displaystyle{\frac{{\sqrt{{{4}}}{\left\lbrace{x}^{{{7}}}\right\rbrace}}}{{\sqrt{{{4}}}{\left\lbrace{x}^{{{3}}}\right\rbrace}}}}$$
Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
$$\displaystyle{\frac{{\sqrt{{{3}}}{\left\lbrace{8}{x}^{{{2}}}\right\rbrace}}}{{\sqrt{{{x}}}}}}$$
Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
$$\frac{\sqrt[3]{8x^{2}}}{\sqrt{x}}$$
Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
a) $$r^{^1/_6}\ r^{^5/_6}$$
b) $$a^{^3/_5}\ a^{^3/_{10}}$$
Simplifying Expressions Involving Radicals Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. NKS $$\displaystyle\sqrt{{{x}^{{{5}}}}}{x}{5}$$
Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. $$\sqrt{x^{5}}$$
The given expression using rational exponents. Then simplify and convert back to radical notation. Assume that all variables represent positive real numbers.
Given:
The expression is $$\displaystyle\sqrt{{{81}{a}^{12}{b}^{20}}}$$
$$\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}$$
a) $$\displaystyle\sqrt{{{6}}}{\left\lbrace{y}^{{{5}}}\right\rbrace}\sqrt{{{3}}}{\left\lbrace{y}^{{{2}}}\right\rbrace}$$
b) $$\displaystyle{\left({5}\sqrt{{{3}}}{\left\lbrace{x}\right\rbrace}\right)}{\left({2}\sqrt{{{4}}}{\left\lbrace{x}\right\rbrace}\right)}$$
An expression: $$\displaystyle\sqrt{{3}}{\left(\sqrt{{27}}-\sqrt{{3}}\right)}$$