Which of the following is equal to x? - Vidyadip

MCQ

Which of the following is equal to x?

A
$x^{\frac{12}{7}}-x^{-\frac{5}{7}}$
B
$\sqrt[12]{\left(x^4\right)^{1 / 3}}$
✓
$\left(\sqrt{x^3}\right)^{2 / 3}$
D
$x^{\frac{12}{7}} \times x^{\frac{7}{12}}$

✓

Answer

Correct option: C.

$\left(\sqrt{x^3}\right)^{2 / 3}$

(c)
We find that $x^{\frac{12}{7}}-x^{-\frac{5}{7}}=x^{\frac{12}{7}}-\frac{1}{x^{5 / 7}}=\frac{x^{\frac{12}{7}} \times x^{\frac{5}{7}}-1}{x^{5 / 7}}=\frac{x^{\frac{12}{7}+\frac{5}{7}}-1}{x^{5 / 7}}=\frac{x^{\frac{17}{7}}-1}{x^{5 / 7}} \neq x$;
$\sqrt[12]{\left(x^4\right)^{1 / 3}}=\left(x^{4 \times \frac{1}{3}}\right)^{\frac{1}{12}}=x^{4 \times \frac{1}{3} \times \frac{1}{12}}=x^{1 / 9} \neq x ; \quad\left(\sqrt{x^3}\right)^{2 / 3}=\left\{\left(x^3\right)^{\frac{1}{2}}\right\}^{\frac{2}{3}}=x^{\frac{3}{2} \times \frac{2}{3}}=x$
and,\[x^{\frac{12}{7}} \times x^{\frac{7}{12}}=x^{\frac{12}{7}+\frac{7}{12}}=x^{\frac{193}{12}} \neq x \]
Hence, option (c) is correct.

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