Repeated Exponentiation

Q. The simplest form of ${27}^2\times 9^{-3}?$ is .

Q. Which of the following option is equal to $8^5?$

1. $2^8$
2. $5^8$
3. $2^{15}$
4. None of the above

Q. If $a$ is an integer other than zero, $p$ and $q$ are integers, then the value of $(a^p{)}^q$ is for $a=2$, $p=3$ and $q=4$?

1. $2^7$
2. $2^{12}$
3. $2^{81}$
4. $2^{34}$

Q. What can $(5^2{)}^3$ be expressed as:

1. $5^6$
2. $5^5$
3. $5^8$
4. $5^9$

Q. $(3^3{x}^5{)}^3$ can be written as $3^9{x}^{15}$

1. True
2. False

Q. Match the first column elements with their correct answers given in the second column.

1. $2^5{x}^{10}{y}^{15}$
2. $x^6{y}^9{z}^{12}$
3. $4^{3x}{6}^{2x}$
4. $7^{4rs}{z}^{6rs}$

Q. What is the value of $x$ for
$(3^3{)}^2\times (2^3{)}^2=x^6$?

1. $6$
2. $4$
3. $9$
4. $8$

Q. Simplify $(2{)}^5\times (5{)}^5$ and write in an exponential form.