Multiplying Exponents with Same Base

Q.

For a non-zero rational number $z$, ${\left(z^{-2}\right)}^3$ is equal to:

1. $z^6$

2. $z^{-6}$

3. $z^1$

4. $z^4$

Q. A certain ball is dropped from a height of 𝑥 feet. It always bounces up to $\frac{2}{3}x$ feet. Suppose the ball is dropped from 10 feet and is stopped exactly when it touches the ground after the 3rd bounce. What is the total distance traveled by the ball? Express your answer in exponential notation.

1. $10+2[10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$
2. $2[10+10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$
3. $2[10\times (2/3)+10\times (2/3{)}^2+10\times \left(2/3{)}^3\right]$
4. $10+10\times \left(2/3\right)+10\times (2/3{)}^2+10\times (2/3{)}^3$

Q. How many more times do we have to fold a piece of paper so that its thickness is twice the distance between the Earth and the Moon?

1. 42
2. 43
3. 1
4. 2

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. Evaluate: $5A^4{B}^5\times 2A{B}^3$

1. $10A^4{B}^8$
2. $10A^5{B}^5$
3. $10A^5{B}^8$
4. $10A^4{B}^{15}$

Q. What is the ninth term in the following sequence of natural numbers: 1, 1+3, 1+3+5, 1+3+5+7, .... ?

1. 81
2. 64
3. 100
4. 49

Q. How many mobile phones can a manufacturer produce in $2,000$ days if it can produce $4\times {10}^5$ phones everyday?

1. $8\times {10}^5$
2. $8\times {10}^8$
3. $8\times {10}^{15}$
4. None of the above

Q. Carl ate $3^5$ jelly beans and at the same time, Buffy ate $5^3$ jelly beans. Who ate more jelly beans?

1. Carl
2. Buffy
3. Both ate equally.
4. Cannot be determined.

Q. Evaluate: $5A^4{B}^5\times 2A{B}^3$

1. $10A^4{B}^8$
2. $10A^5{B}^5$
3. $10A^5{B}^8$
4. $10A^4{B}^{15}$

Q. How many more times do we have to fold a piece of paper so that its thickness is twice the distance between the Earth and the Moon?

1. 42
2. 43
3. 1
4. 2

Q. Let $a$ be a non-zero number. Select the pairs which on division would give $a^2$ as the answer.

1. $a^9$
2. $a^8$
3. $a^7$
4. $a^6$
5. $a^{19}$
6. $a^{17}$

Q. What would be the value of $x$ for the equation $5^x=\frac{1}{125}$ ?

1. -2
2. -3
3. 4
4. 5

Q. Arrange the following numbers in increasing order of their values.

1. $1.01$ x ${10}^7$
2. $2.1$ x ${10}^8$
3. $0.3$x${10}^{10}$
4. $0.8$x${10}^{12}$

Q. Select the pair which on multiplication gives $A^{1/20}$ as the possible answer.

1. $A^{1/5}$
2. $A^{1/2}$
3. $A^{1/4}$
4. $A^{1/10}$
5. $A^0$
6. $A^{1/20}$

Q. Select all the expression(s) with same base.

1. $7^3$
2. $3^7$
3. $5^3$
4. $7^2$

Q.

Represent $5^2\times 3^2$ as a single exponent.

Q. Select the option that would be equal to $9^8$.

1. $9^4\times 9^2$
2. $9^4\times 9^4$
3. $9^4\times 9^6$
4. $9^4\times 9^5$

Q. Write an equivalent expression for the following problem:
$5^5$x $5^2$

1. $5^{10}$
2. $5^7$
3. $5^3$
4. ${25}^2$

Q.

Write ${12}^6÷{12}^4$ as a single exponent.

Q. What would be the value of $x$ for the equation $2^{-x}=2^7$ ?

1. -5
2. -7
3. 5
4. 7

Q. Select the following expression(s) which is(are) equal to $16\times 2^4.$

1. $2^4\times 2^4$
2. $2^8$
3. $512$
4. $256$