Simplify the following and express your answer in the exponential notation.

$3^5\times 3^7$

Simplify the following and express your answer in the exponential notation.

$2^{10}÷2^6$

Simplify the following and express your answer in the exponential notation.

${\left(5^2\right)}^4$

Simplify the following and express your answer in the exponential notation.

${\left(6^3\right)}^7$

Simplify the following and express your answer in the exponential notation.

${\mathrm{a}}^4\times {\mathrm{a}}^7$

Simplify the following and express your answer in the exponential notation.

${\mathrm{c}}^8÷{\mathrm{c}}^5$

Simplify the following and express your answer in the exponential notation.

${\left({\mathrm{e}}^4\right)}^5$

Simplify the following and express your answer in the exponential notation.

${\left({\mathrm{f}}^7\right)}^3$

Evaluate the following.

$2^0-2^{-3}$