Division Rules of Exponents

Q.

What is the value of $3^{-2}$?

Q.

Say true or false and justify your answer:$3^0={\left(1000\right)}^0$

1. True
2. False

Q. Match column I with column II and select the correct answer by using the given codes.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ & & & \\ \text{(A)}& \frac{9^6}{(27{)}^6}\times 3^3& \text{(P)}& 3\\ & & & \\ & & & \\ \text{(B)}& \frac{{16}^3}{8^3}\times 2^2& \text{(Q)}& 27\\ & & & \\ & & & \\ \text{(C)}& \frac{2^3\times (12{)}^4}{4^4\times 6^3}& \text{(R)}& 32\\ & & & \\ & & & \\ \text{(D)}& \frac{{12}^5}{4^5}\times \frac{1}{3^2}& \text{(S)}& \frac{1}{27}\\ & & & \end{array}$

1. $A\to P;B\to Q;C\to R;D\to S$
2. $A\to Q;B\to P;C\to R;D\to S$
3. $A\to S;B\to P;C\to R;D\to Q$
4. $A\to S;B\to R;C\to P;D\to Q$

Q. Find the value of $\frac{5^5}{{10}^5}$.

1. $\frac{1}{32}$
   
2. $\frac{1}{16}$
   
3. $\frac{1}{8}$
   
4. $32$
5. $16$

Q. The value of $\frac{x^2{y}^9}{x^7{y}^5}$ is

1. $\frac{y^4}{x^5}$
2. $\frac{x^4}{y^5}$
3. $\frac{y^5}{x^4}$
4. $\frac{x^5}{y^4}$

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

1. $3^{10}$
2. $3^8$
3. $3^7$
4. $3^{12}$

Q. Choose the correct expression(s).

1. $\frac{5^{2025}}{5^{2021}}=5^4$
2. $\frac{5^{2021}}{{10}^{2021}}=(\frac{1}{2}{)}^{2021}$
3. $\frac{{25}^{1011}}{6^{2022}}=(\frac{5}{6}{)}^{2022}$

Q. What is the value of $\frac{3^4}{3^6}$?

1. $9$
2. $\frac{1}{9}$
3. $3$
4. $\frac{1}{3}$

Q. The value of $\frac{14a^7}{2a^7}$ is

1. $1$
2. $7$
3. $14$
4. $0$

Q. $\frac{3^{21}}{3^{17}}+\frac{2^{73}}{2^{72}}=$

1. $85$
2. $79$
3. $83$
4. $81$

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

1. $5$
2. $1$
3. $\frac{1}{64}$
4. $9$

Q. The value of $\frac{(16{)}^5}{(12{)}^5}\times \frac{(24{)}^5}{(32{)}^5}$ is

Q. If $S=1^0+2^0+3^0+4^0+\dots +{50}^0,$ then the value of $S$ is

1. $0$
2. $1^{50}$
3. $50$
4. $100$

Q. Which of the following is equal to $\frac{15x^6{z}^5}{5x^{3}z}?$

1. $3x^3{z}^4$
2. $3x^3{z}^5$
3. $3x^4{z}^3$
4. None of the above

Q. Which of the following is the simplest form of $\frac{9^{\frac{5}{2}}}{4^5}?$

1. Not possible to simplify
2. $(\frac{9}{4}{)}^5$
3. $(\frac{3}{4}{)}^5$
4. $(\frac{3}{4}{)}^{\frac{25}{2}}$