Question

Evaluate the expression $(-x{)}^3\times (-x{)}^2$ for $x=\frac{2}{3}.$

• A. $-\frac{32}{27}$
• B. $\frac{64}{81}$
• C. $-\frac{32}{243}$
• D. $\frac{32}{81}$

Answer 1

The correct option is C $-\frac{32}{243}$

$\because a^m\times a^n=a^{(m+n)},$
$(-x{)}^3\times (-x{)}^2=(-x{)}^{3+2}=(-x{)}^5$
$=(\frac{-2}{3}{)}^5$
But, $(\frac{-2}{3}{)}^{-5}=\frac{(-2{)}^5}{(3{)}^5}(\because (\frac{a}{b}{)}^m=\frac{a^m}{b^m})$
$=-\frac{32}{243}.$
$\therefore (-x{)}^3\times (-x{)}^2$ for $x=\frac{2}{3}$ has the value $-\frac{32}{243}.$