Powers and Exponents

Q.

Bacteria can divide in every 20 minutes. So, 1 bacterium can multiply to 2 in 20 minutes, 4 in 40 minutes, and so on. How many bacteria will there be in 6 hours? Write your answer using exponents, then evaluate.

Q.

What is $\frac{3\mathrm{\pi }}{4}$ in degrees?

Q.

Divide: $16\sqrt{6}$ by $4\sqrt{2}$.

Q.

Express each of the following as a product of prime factors only in exponential form: $270$

Q.

Question 5(ii)
Express each of the following as product of powers of their prime factors:
(ii) 405

Q.

If a = 2 and b = 3, find the value of $a^b$.

1. 16

2. 32

3. 64

4. 8

Q.

Question 5(iii)
Express each of the following as product of powers of their prime factors:
(iii) 540

Q.

Question 80 (b)

Express each of following as a product of powers of their prime factors.
2025

Q. If $x=3-2\sqrt{2}$, find $x^2+\frac{1}{x^2}$.

Q.

Express each of following as a product of powers of their prime factors: $9000$

Q.

The value of$(8^{-25}-8^{-26})$ is

1. $7\times 8^{-25}$

2. $7\times 8^{-26}$

3. $8\times 8^{-26}$

4. None of the above

Q. If $(-2{)}^x=-128$, then find the value '$x$'.

1. $5$
2. $10$
3. $3$
4. $7$

Q.

Simplify and express each of the following in exponential form:$({\left(5^2\right)}^3\times 5^4)÷5^7$

Q.

Express the following in power notation and exponential form :

$\frac{-729}{64}$.

Q.

Question 80 (c)

Express each of following as a product of powers of their prime factors.
800

Q.

$625$ expressed as a power of $5$

Q.

Question 21

Which of the following is not true?
(a)$3^2>2^3$
(b)$4^3=2^6$
(c)$3^3=9$
(d)$2^5>5^2$

Q. Write the equation for the following statement:
Ten times $a$ is 70.

1. 10$a$ = 70
2. $a$ - 10 = 70
3. $a$ + 10 = 70
4. $\frac{10}{a}$ = 70

Q.

Question 78 (c)

Express each fo the following numbers using exponential notations
$\frac{144}{875}$

Q.

Express 140 as product of its prime factors.

Q. Question 1 (i)
Express each number as the product of its prime factors:
(i) 140

Q. Question 94:

Blubber makes up 27 per cent of a blue whale's body weight. Deepak found the average weight of blue whales and used it to calculate the average weight of their blubber. He wrote the amount as $2^2\times 3^2\times 5\times 17kg.$ Evaluate this amount.

Q.

Question 1(iii)
Find the value of:
(iii) ${11}^2$

Q. By what number should we multiply $\frac{6}{\frac{2}{3}}$ to get $\frac{25}{\frac{5}{6}}$?

Q.

Question 76 (a)

Express the following in exponential form.
$3\times 3\times 3\times a\times a\times a\times a$

Q.

Question 78 (b)

Express each fo the following numbers using exponential notations.
1029

Q. The multiplicative inverse of $2^2$ is $\frac{1}{4}$.

1. False
2. True

Q. In 2n, n is known as a/an .

1. base
2. exponent
3. constant
4. alphabet

Q.

If $1125=3^x\times 5^y$ then find the value of $x+y$.

1. 2

2. 3

3. 5

4. 1

Q. ‘2’ multiplied ten times is expressed numerically as _____ .

1. $2\times 10$
2. $2\times 2\times 2\text{....10 times}$
3. $2^{10}$
4. $\frac{2}{10}$