Powers and Exponents

Q. The sum of the exponents of the prime factors in the prime factorisation of 196, is

(a) 1
(b) 2
(c) 4
(d) 6

Q.

Question 3(iii)
Express the number appearing in the following statements in standard form:
Size of bacteria is 0.0000005 m.

Q.

Express the product of $3.2\times {10}^6$ and $4.1\times {10}^{-1}$ in the standard form.

Q. 34. Find the exponent of 12 in 100 factorial

Q.

Question 179(ii)

Express each of the following in exponential form.
$\frac{-125}{343}$

Q.

Question 179(iii)

Express each of the following in exponential form.
$\frac{400}{3969}$

Q. In how many ways can the number $7056$ be resolved into two factors?

Q. Write the sum of exponents of the prime factors in the prime factorisation of 250.

Q.

write the exponents of 2 in prime factorization of 144?

Q. $(x^2-xy+y^2)(x+y)$

Q. Which of the following units can be compared?

1. $kg:cm$
2. $m:kg$
3. $cm:m$
4. $hour:kg$

Q. If $9^{x+2}=240+9^x$, then $x=$

1. $0.5$
2. $0.2$
3. $0.4$
4. $0.6$

Q. Find the exponent of 2 and 5 in 1)15! 2)22! 3)32! 4)43! 5)52! 6)100! 7)75! 8)85! 9)90! 10)150

Q. Find out the value of '?':

1. $10$
2. $8$
3. $11$
4. $9$

Q. How can one obtain the number of digits where the exponents are very large?Say , how to obtain the number of digits in the product of 8^32 and 5^55?

Q.

Question 89

In the following question, state whether the given statements are true (T) or false (F).

Large numbers can be expressed in the standard form by using positive exponents.

Q. Find the product of:$(x-2)(x+2)(x^2+4)(x^4+16)$

1. True
2. False

Q.

Write down each of the following in the exponential form.

$4x^3\times 9x^{2}y\times 5y^2$

Q. The value of $\frac{{(a-b)}^3+{(b-c)}^3+{(c-a)}^3}{(a-b)(b-c)(c-a)}$ is

1. $1$
2. $3$
3. $\frac{1}{3}$
4. zero

Q. write the exponent of 3 in the prime factorisation of 162

Q. Find the square of rational number $\frac{13}{26}$.

1. $\frac{169}{676}$
2. $\frac{144}{169}$
3. $\frac{169}{576}$
4. $\frac{13}{26}$

Q. IF $\frac{5x+6y}{5u+6v}=\frac{5x-6y}{5u-6v}$
Then prove that x: y = u: v