Exponential Form of a Number

Q.

Express:
(iii) $81$ as a power of $3$

Q. Express each of the following as a product of prime factors only in exponential form:
(i) 729 × 64 (ii) 768

Q. Express $6\times 6\times 6\times 6$ in exponential form as a base 6.

Q. Simplify $\frac{a{b}^2{c}^3\times a^4{b}^5{c}^{-6}}{a^{-7}{b}^{-8}{c}^9\times a^{10}{b}^{11}{c}^{-12}\times a^{13}{b}^{-14}{c}^{15}}$

1. $a^{11}{b}^{18}{c}^{-15}$
2. $a^{11}{b}^{18}{c}^{15}$
3. $a^{-11}{b}^{18}{c}^{-15}$
4. $a^{-11}{b}^{-18}{c}^{15}$

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

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

Q.

Using$(x+a)(x+b)=x^2+(a+b)x+ab$, find $(103x104)$

Q. Express the following numbers using exponential notation
(i) $3125$
(ii) $343$

Q.

Express 32000 as a product of powers of prime factors.

1. $2^8\times 5^2$

2. $2^8\times 5^3$

3. $2^7\times 5^4$

4. $2^8\times 5^4$

Q. Which among the following is equal to​ 2^2 x 3^2 ?

1. 5^2
2. 2^4
3. 2^6
4. 6^2

Q.

Find the value of

$(2\times {10}^4)+(3\times {10}^3)+(1\times {10}^2)+(6\times {10}^1)+(7\times {10}^0)+(4\times {10}^{-1})+(2\times {10}^{-2})+(8\times {10}^{-3})$

1. 2316.7428

2. 43210.123

3. 23167.428

4. 23167428

Q. Express $6\times 6\times 6\times 6$ in exponential form.

Q. Express the given statement in exponential form.
3 is multiplied by itself 7 times.

1. $3^7$
2. $3^{-7}$
3. $3^5\times 3$
4. $3\times 7$

Q. (3²)³ =

1. 6⁵
2. 3⁵
3. 3⁸
4. 3⁶

Q. Arrange them in ascending order.

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

Q.
What is the output when input is a = 3 and b = 8?

1. 3, 8
2. 8, 3
3. 4, 9
4. 9, 4

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

1. 
2. 
3. 

Q. Simplify the following and write the answer in the
exponential form.
$\left[\right(2^2{)}^3\times 3^6]\times 5^6$

Q. Express $6\times 6\times 6\times 6$ in exponential form.

Q.

Write the following in the expanded notation

$291.007$

Q. Which of the four images represents $2^3$?

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

Q.

Write the following in the expanded notation

$75.032$

Q. If we represent 343 in exponential form , then the base is and the exponent is .

1. 7
2. 3
3. 9
4. 19

Q.

Write the following in the expanded notation

$11.095$

Q.

$3\times 1000+2\times 10+\frac{4}{10}+\frac{3}{1000}$is the expanded form of the number ____.

1. $3002.403$

2. $32.430$

3. $3200.430$

4. $3020.403$

Q. Find the number from each of the following expanded forms:
(i) $7\times {10}^4+6\times {10}^3+0\times 0^2+4\times {10}^1+5\times {10}^0$
(ii) $5\times {10}^5+4\times {10}^4+2\times {10}^3+3\times {10}^0$

Q. Express $6\times 6\times 6\times 6$ in exponential form.

Q. Expanded form of 51280 is $5\times {10}^4+1\times {10}^a+2\times {10}^2+8\times {10}^b+0$.
Find the value of a and b.

1. a=3, b=1
2. a=3, b=2
3. a=1, b=3
4. a=4, b=2

Q.

Simplify:
$-2+8÷4$

Q. Which of the following is the expanded form of 2831.

1. $2\times {10}^3+8\times {10}^2+3\times {10}^1+1\times {10}^0$
   
2. $2\times {10}^3+8\times {10}^2+3\times {10}^2+1\times {10}^1$
3. $2\times {10}^3+3\times {10}^2+8\times 10+1\times {10}^0$
4. $2\times {10}^3+3\times {10}^2+8\times {10}^2+1\times {10}^1$

Q. Which of the following is the expanded form of 2831.

1. $2\times {10}^3+8\times {10}^2+3\times {10}^2+1\times {10}^1$
2. $2\times {10}^3+8\times {10}^2+3\times {10}^1+1\times {10}^0$
   
3. $2\times {10}^3+3\times {10}^2+8\times {10}^2+1\times {10}^1$
4. $2\times {10}^3+3\times {10}^2+8\times 10+1\times {10}^0$