Question

Choose the correct word/answer and fill in the blanks :

$\left(3^6÷3^2\right)\times 3^5=\_\_\_\_\_\_\_\_(3^9/3^{\frac{6}{2}+5})$

Answer 1

Compute the required value:

By the properties of exponent, we know that -

$$\begin{gathered} a^x\times a^y=a^{x+y} \\ {a}^x÷a^y=a^{x-y} \end{gathered}$$

By using the above properties -

$$\begin{gathered} \left(3^6÷3^2\right)\times 3^5=3^{6-2}\times 3^5 \\ =3^4\times 3^5 \\ =3^{4+5} \\ =3^9 \end{gathered}$$

Hence, the correct answer is $3^9$.