Question

The value of $3^5÷3^{-6}$ is

• A. $3^5$
• B. $3^{-6}$
• C. $3^{11}$
• D. $3^{-11}$

Answer 1

The correct option is C

$3^{11}$

Find the value of$3^5÷3^{-6}$

By the law of exponents,

$\frac{a^m}{a^n}=a^{m-n}$

$\begin{array}{rcl}{3}^5÷3^{-6}& =& \frac{3^5}{3^{-6}}\\ & =& 3^{5-\left(-6\right)}\\ & =& 3^{5+6}\\ & =& 3^{11}\\ \therefore 3^5÷3^{-6}& =& 3^{11}\end{array}$

$\therefore$The correct option is C.