Question

which of the following is equal to x²
$a )x \frac{12}{7} - x \frac{5}{7} \\ b) \sqrt[12]{ ({x}^{4}) } \frac{1}{3} \\ c)( \sqrt{ {x}^{3} } ) \frac{2}{3} \\ d)x \frac{2}{4} \times x \frac{6}{4}$
​

Answer 1

$\text{Consider,}$

$x^{\frac{2}{4}}{\times}x^{\frac{6}{4}}$

$\text{Using,}$

$\boxed{\bf\,a^m\,a^n=a^{m+n}}$

$\text{we get}$

$=x^{\frac{2}{4}+\frac{6}{4}}$

$=x^{\frac{2+6}{4}}$

$=x^{\frac{8}{4}}$

$=x^2$

$\implies\bf\,x^{\frac{2}{4}}{\times}x^{\frac{6}{4}}=x^2$

$\therefore\textbf{Option (D) is correct}$