Sum of Powers

Q. Solve the following equation by trial and error method:
$3m-14=4$

Q. $3^8$ is equal to

1. $6561$
2. $19683$
3. $2187$
4. $729$

Q.

$2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}+2^{11}$ =___

1. $2^{11}-2$

2. $2^{12}-2$

3. $2^{11}-1$

4. $2^{12}-1$

Q. The number that can be split like:
$(1\times 100)+(1\times 10)+(1\times 9)+(3\times {10}^{-1})+(6\times {10}^{-2})+(7\times {10}^{-3})$ is

1. 1.19367
2. 1193.67
3. 11.9367
4. 119.367

Q.

$2+2^2+2^3+2^4+2^5+2^6$ =___

1. $2^7-1$

2. $2^6-1$

3. $2^6-2$

4. $2^7-2$

Q. Sum of numbers $2+2^2+2^3+2^4+2^5$ is

1. $62$
2. $64$
3. $60$
4. $66$

Q. Match the powers with their corresponding numbers.

1. 2000
2. 8000
3. 800
4. 400

Q.

$\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}+\frac{1}{2^9}$=___

1. $1-\frac{1}{2^6}$

2. $1-\frac{1}{2^5}$

3. $1-\frac{1}{2^9}$

4. $2-\frac{1}{2^9}$

Q. Sort the following numbers in increasing order from top to bottom.

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

Q. $9\times 9\times 9\times 9\times 9\times 9\times 9$ can be written as $7^9$.

1. False
2. True

Q. $9\times 9\times 9\times 9\times 9\times 9\times 9$ can be written as $7^9$.

1. True
2. False

Q. Fill in the blanks to make the following statements true:
$[13+(-12\left)\right]+(...)=13+\left[\right(-12)+(-7\left)\right]$.

Q.

Using power law simplify $(x^6{)}^{\frac{3}{2}}$

1. x¹⁸

2. x¹²

3. x⁶

4. x⁹

Q.

$\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}$=___

1. $1-\frac{1}{2^6}$

2. $1-\frac{1}{2^7}$

3. $1-\frac{1}{2^3}$

4. $1-\frac{1}{2^4}$

Q. $9\times 9\times 9\times 9\times 9\times 9\times 9$ can be written as $7^9$.

1. True
2. False

Q. $1^1$ can be expressed as ${10}^0$.

1. True
2. False

Q. Find three numbers in A.P. whose sum and products are respectively $36$ and $1620$

Q. Subtract :
$\frac{-16}{21}$ from $1$

Q. Which expression is not equivalent to $3\times 3\times 3\times 3\times 3\times 3$?

1. $3^6$
2. 18
3. $9^3$
4. 729

Q. $\text{The sum of the powers}$
$\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}$
$\text{can be written as}=1-\frac{1}{2^4}$

1. False
2. True

Q. $\text{The sum of the powers}$
$2+2^2+2^3+2^4+2^5+2^6$
$\text{can be written as}$ $=2^7-1$.

1. False
2. True