Question

Evalute the following expression $(x^2{)}^{2x-6}-{(2x-6)}^{x^2}$ for $x=3.$

• A. 9
• B. 6
• C. 1
• D. 0.0

Answer 1

The correct option is C 1

$(x^2{)}^{2x-6}=x^{2\times (2x-6)}(\because (a^m{)}^n=a^{mn})$
$=x^{4x-12}$
Since $x=3,$
$(x^2{)}^{2x-6}=x^{4x-12}$
$=3^{4\left(3\right)-12}$
$=3^{12-12}$
$=3^0$
$=1(\because a^0=1)$
Also, $(2x-6{)}^{x^2}=(2\left(3\right)-6{)}^{3^2}$
$=(6-6{)}^9$
$=0.$
$\therefore (x^2{)}^{2x-6}-{(2x-6)}^{x^2}=1-0=1$