Question

# To calculate: The expression with the help of rational exponents sqrt{11t}

To calculate: The expression with the help of rational exponents $$\displaystyle\sqrt{{{11}{t}}}$$

2021-02-26
Calculation:
Consider the expression, $$\displaystyle\sqrt{{{11}{t}}}$$.
Use the property, $$\displaystyle\sqrt{{{n}}}{\left\lbrace{a}^{{{m}}}\right\rbrace}={a}^{{^{\left\lbrace{m}\angle{n}\right\rbrace}}}.$$
Here, $$\displaystyle{m}={1}\ \text{and}\ {n}={2}$$
Then, the expression $$\displaystyle\sqrt{{{11}{t}}}$$ can be written as
$$\displaystyle\sqrt{{{11}{t}}}=\sqrt{{{\left({11}{t}\right)}}}$$
$$\displaystyle={\left({11}{t}\right)}^{{^{\left\lbrace{1}\angle{2}\right\rbrace}}}$$
Thus, the required expression is $$\displaystyle{\left({11}{t}\right)}^{{^{\left\lbrace{1}\angle{2}\right\rbrace}}}.$$