Division Rules of Exponents

Q.

What is $2$ raised to the power of $100$?

Q.

Find the value of $216$ to the power of $\frac{-2}{3}$

Q.

$a^m\times a^n$ is equal to

1. $a^{m+n}$

2. $a^{m-n}$

3. $a^{mn}$

4. $a^{n-m}$

Q.

$i+i^2+i^3+i^4+....+i^{100}$ equals:

1. $-1$

2. $0$

3. $1$

4. None

Q. The amount left after $N$ half lives equals $\frac{1}{2^N}$ times the beginning amount.

1. True
2. False

Q.

Simplify $8^{\frac{2}{3}}$.

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. A rectangular area of land is being sold off in smaller pieces. The total area of the land is $2^{15}$ square miles. The pieces being sold are $8^3$ square miles in size. How many smaller pieces of land can be sold at the stated size? Compute the actual number of pieces.

1. $32$
2. 64
3. 128
4. 16

Q. The radioactive substance Mathium has a half-life of 1 minute. If we have 32 pounds of Mathium at the start, how long will it take us to have only 4 ounces of Mathium left?

1. 6 minutes
2. 7 minutes
3. 8 minutes
4. 9 minutes

Q. What is the simplest form of the expression $\frac{16x^{16}}{2x^2}$ ?

1. $8x^{14}$
2. $8x^8$
3. $8x^{18}$
4. None of the above

Q. A magical basket has the power to double anything kept inside it in one day. June placed 2 apples in the basket on Sunday. On which day will the number of apples in the basket be half of the number of apples on Saturday?

1. Wednesday
2. Thursday
3. Friday
4. Sunday

Q.

What is $2^{\frac{4}{3}}$equal to?

Q. If $2^{-m}\times \frac{1}{2^m}=\frac{1}{4}$, then $\frac{1}{14}\left[\right(4^m{)}^{\frac{1}{2}}+{\left(\frac{1}{5^m}\right)}^{-1}]$, is equal to

Q. $\text{What is the value of}(\frac{4}{3}{)}^{-2}$ ?

1. $\frac{16}{9}$
2. $\frac{9}{16}$
3. $\frac{-16}{-9}$
4. None of the above

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

1. $2^4$
2. $2^4\times 3^4$
3. $2^8\times 3^8$
4. $2^6\times 3^6$

Q. What is the breadth of a rectangular park with $15x^6{z}^5$ unit${}^2$ area and length $5x^3{z}^4$ units?

1. $3x^3{z}^4$
2. $3x^{3}z$
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. $(\frac{3}{4}{)}^{\frac{25}{2}}$

Q. $a^0(a\ne 0)$ would always be equal to 1.

1. True
2. False

Q. What would be the value of the expression $(-2{)}^4\times (2{)}^{-2}$?

1. 64
2. 32
3. 4
4. 8

Q. For $a,b\ne 0,$ select the correct statement(s).

1. $\frac{a^m}{a^n}=a^{m-n}$
2. $\frac{a^m}{a^n}=a^{\frac{m}{n}}$
3. $\frac{a^n}{b^n}={\left(\frac{a}{b}\right)}^n$
4. $\frac{a^n}{b^n}=\frac{a}{b}$

Q.

Express ${\left(2^3\right)}^7$as power of prime numbers.

Q. The radioactive substance Mathium has a half-life of 1 minute. If we have 32 pounds of Mathium at the start, how long will it take us to have only 4 ounces of Mathium left?

1. 6 minutes
2. 7 minutes
3. 8 minutes
4. 9 minutes

Q.

Simplify and express the result in power of $3$ :

$\left(4^2\times 4^3\right)÷4^5$.

Q. Select the bubbles that give negative exponent after simplification.

1. $5^2/5^2$
2. $2^5/2^7$
3. $1/1^{12}$
4. $8/8^3$
5. $7/7^5$
6. $7/7^2$
7. $9/9^3$
8. $9^2/9$

Q. Uranium-235 has a half-life of 3 minutes. A fresh sample weighing 80 pounds was obtained. If it takes 15 minutes to set up an experiment using Uranium-235, how much Uranium-235 will be left when the experiment begins?

1. $0.25$ pounds
2. $2.5$ pounds
3. $25$ pounds
4. $80$ pounds

Q. Select the pair of numbers having the same exponents.

1. $1/(12{)}^{-7}$
2. $9^{-6}$
3. $4^5$
4. $8^7$
5. $(-10{)}^5$
6. $1/2^6$

Q. Which of the following is equal to $\frac{8^3}{4^2}?$

1. $2$
2. $2^3$
3. $2^4$
4. $2^5$