Question

Evaluate: ${\left[\right(x^y{)}^{1-\frac{1}{y}}]}^{\frac{1}{y-1}}$

• A. $x$
• B. $y$
• C. $\frac{1}{x}$
• D. $\frac{1}{y}$

Answer 1

Answer: (A)

$x$

${\left[\right(x^y{)}^{1-\frac{1}{y}}]}^{\frac{1}{y-1}}$$={\left[\right(x^y{)}^{\frac{y-1}{y}}]}^{\frac{1}{y-1}}={\left[x^{y\times \frac{y-1}{y}}\right]}^{\frac{1}{y-1}}$
$=x^{y-1\times \frac{1}{y-1}}=x^1=x$