Visualising Powers and Exponents

Q.

How do you simplify ${\left(81\right)}^{\frac{3}{4}}$?

Q. 1. In a basket there are 1250 flowers. A man goes for worship and puts as many flowers as there are temples in the city. Thus he needs 8 baskets of flowers. Find the number of temples in the society.
2. Find the least number of six digits which is a perfect square.

Q. The exponential form of $\sqrt{\sqrt{2}+\sqrt{3}}$ is:

1. $6$
2. $(6{)}^{\frac{1}{2}}$
3. $(6{)}^{\frac{1}{4}}$
4. $(6{)}^{\frac{-1}{2}}$

Q.

Simplify and express each of the following in exponential form: $\frac{3^7}{(3^4\times 3^3)}$.

Q. , 3 raise to power minus 5 x 15 Square x 25 /5 raised to 4
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Q. By what number should we multiply $4^{-3}$ so that the product may be equal to 64?

1. $4^5$
2. $2^{12}$
3. $2^6$
4. None of these

Q.

Simplify and express in exponential form:

${\left(\frac{3}{7}\right)}^5\times {\left(\frac{2}{5}\right)}^5$.

Q. The exponential form of $\sqrt{\sqrt{2}\times \sqrt{3}}$ is

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

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

3. $6^{\frac{1}{4}}$

4. $6$

Q.

What is the meaning of surds

Q.

Express $104972$ using powers of $10$ in exponent form.

Q.

Question 55

In the following question, fill in the blanks to make the statements true.

The standard from for 32500000000 is ___ .

Q. In the figure given below, each small square represents $3^0$. Which colour represents $3^1$ ?

1. Yellow
2. Green
3. Purple
4. Red

Q. By what number should we multiply $4^{-3}$ so that the product may be equal to 64?

1. None of these
2. $2^{12}$
3. $2^6$
4. $4^5$

Q.
Which of the above represents $2^4$ pencils?

1. B
2. C
3. D
4. A

Q. What will be the exponent of 10, if we write 1250000 in standard form?

1. 7
2. 8
3. 6
4. 5

Q. Which of the four images represents $2^4$?

1. A
2. B
3. C
4. D

Q.

Question 47

In the following question, fill in the blanks to make the statements true.

The standard from of 12340000 is ___ .

Q.

How do you write $7.4x{10}^{-5}$ in standard notation?

Q. The standard notation of 1650000 is given by .

1. $1.65\times {10}^{13}$
2. $16.5\times {10}^8$
3. $1650\times {10}^7$
4. $1.65\times {10}^6$

Q. The exponential form of $\sqrt{\sqrt{2}}\times \sqrt{\sqrt{3}}$

1. $6^2$
2. $6^{\frac{1}{2}}$
3. $6^{\frac{1}{4}}$
4. $6$

Q. Which one of the following is not equivalent to $0.000000375$ ?

1. $3\frac{3}{4}\times {10}^{-7}$
   
2. $375\times {10}^{-9}$
   
3. $3.75\times {10}^{-7}$
   
4. $\frac{3}{8}\times {10}^{-7}$
   

Q.

Simplify and express each of the following in exponential form :

(vi) $\frac{3^7}{3^4\times 3^3}$

Q. The standard notation of 1650000 is given by .

1. $1.65\times {10}^{13}$
2. $16.5\times {10}^8$
3. $1650\times {10}^7$
4. $1.65\times {10}^6$

Q.

Question 102

By what number should we multiply $(-29{)}^0,$ so that the product becomes $(+29{)}^0$

Q. In the given figure, each small square represents $2^0$.
Which of the following combinations of colours represent $2^3$?

1. Yellow, blue and red
2. Yellow, dark green, blue and purple
3. Blue, purple, red and light green
4. Purple and light green

Q. By what number should we multiply $4^{-3}$ so that the product may be equal to 64?

1. $4^5$
2. $2^{12}$
3. $2^6$
4. None of these

Q. Identify the region which represents the power $2^2.$

1. 
2. 
3. 

Q. The standard notation of 1650000 is given by .

1. $1650\times {10}^7$
2. $16.5\times {10}^8$
3. $1.65\times {10}^{13}$
4. $1.65\times {10}^6$

Q. By what number should we multiply $4^{-3}$ so that the product may be equal to 64?

1. $4^5$
2. $2^{12}$
3. $2^6$
4. None of these

Q. Question 83 (xiv)

Multiply the following:
$-\frac{100}{9}rs;\frac{3}{4}{r}^3{s}^2$