Question

$\text{Simplify}\frac{(-3{)}^3\times (-3{)}^7}{3\times 9^6}$

• A. 27
• B. $\frac{1}{27}$
• C. $\frac{2}{3}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B

$\frac{1}{27}$

$\frac{(-3{)}^3\times (-3{)}^7}{3\times 9^6}=\frac{(-3{)}^{3+7}}{3\times (3^2{)}^6}\{\because a^m\times a^n=a^{m+n}\}$
$\Rightarrow \frac{(-3{)}^{10}}{3\times 3^{12}}\{\because (a^m{)}^n=a^{m\times n}\}$
$\Rightarrow \frac{(-3{)}^{10}}{3^{13}}=3^{10-13}=3^{-3}=\frac{1}{3^3}=\frac{1}{27}(\because a^m÷a^n=a^{m-n}and(-3{)}^{10}=3^{10})$