Exponent of an Exponent

Q.

When $x^4+x^3-2x^2+x+1$ is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

1. $x^3+2x^2+x+1$

2. $x^3+x^2+x$

3. $x^3+2x^2+1$

4. $x^3+x^2+1$

Q.

Question 97:

What's the error?
A student said that $\frac{3^5}{9^5}$ is the same as $\frac{1}{3}$. What mistake has the student made?

Q. Choose the incorrect options.

1. $x^{-4}\times x^{-2}=x^8$
2. $\frac{x^5}{x^3}=x$
3. $(x^2{)}^4=x^{2^4}$
4. $2x^{-1}=\frac{1}{2x}$

Q. Match the following.

1. $a^{m+n}$
2. $a^{m-n}$
3. $a^{mn}$

Q.

State true or false
$a^m$ $\times$ $a^n$ = $a^{mn}$

1. True

2. False

Q.

Question 27

In the following question, out of the four options, only one is correct. Write the correct answer.

${\left(\frac{1}{10}\right)}^0$ is equal to

(a) 0

(b) $\frac{1}{10}$

(c) 1

(d)10

Q. $a^{m-n}$ equals

1. $\frac{a^{-m}}{a^n}$
2. $\frac{a^m}{a^{-n}}$
3. $\frac{a^m}{a^n}$
4. $\frac{a^n}{a^m}$

Q. The value of $(2^2{)}^2+(3^2{)}^2$=.

1. 97
2. 98
3. 79
4. 99

Q. $\text{Find the product of the}p\text{and}{q}^2.$

1. $p{q}^2$
2. $pq$
3. $p^2{q}^2$
4. $p^{2}q$

Q.

Question 31

In the following question, out of the four options, only one is correct. Write the correct answer.

For a non-zero rational number$z,(z^{-2}{)}^3$ is equal to:

(a) $z^6$

(b) $z^{-6}$

(c) $z^1$

(d) $z^4$

Q. $(2^{-3}{)}^{-2}$ =

1. $2^6$
2. $2^{-6}$
3. $2^{-5}$
4. $2^{-5}$

Q. What is the multiplicative inverse of $3^{-5}$?

1. $243$
2. $-\frac{1}{243}$
   
3. $-243$
4. $\frac{1}{243}$

Q.

Question 38

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

The value of ${\left(\frac{1}{2^3}\right)}^2$is equal to ___

Q. $(\frac{8^2}{8^5}{)}^4\times 8^{-3}$ = ___

1. $8^2$
2. $8^{25}$
3. $8^{-10}$
4. $8^{-15}$

Q.

Question 30

In the following question, out of the four options, only one is correct. Write the correct answer.

For a non-zero rational number $p^{13}÷p^8$ is equal to :

(a) $p^5$

(b) $p^{21}$

(c) $p^{-5}$

(d) $p^{-19}$

Q.

Question 60

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

The value of $[3^{-1}\times 4^{-1}{]}^2$ is ___ .

Q.

Question 79

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

The value of $\frac{1}{4^{-2}}=16$

Q. The difference of the squares of two consecutive even natural numbers is 92. Taking x as the smaller of the two numbers, form an equation in x, and hence find the larger of the two numbers.

1. $18$
2. $24$
3. $21$
4. $23$

Q. Evalute the following expression $(x^2{)}^{2x-6}-{(2x-6)}^{x^2}$ for $x=3.$

1. 9
2. 6
3. 1
4. 0

Q. Choose the greatest number of the lot.

1. $(5^{-1}{)}^2$
2. $(5^{-2}{)}^{-1}$
3. $(3^{-2}{)}^{-1}$
4. $(2^2{)}^{-5}$

Q.

Simplify and write in exponential form: $4^3\times 4^{-2}\times {16}^2$

1. 4⁶

2. 4³

3. 4⁴

4. 4⁵

Q. The value of $(2^2{)}^{-3}$ is ___.

1. $32$
2. $\frac{1}{64}$
3. $\frac{1}{2}$
4. $256$

Q. The exponent of $c$ after simplifying $\left(7a^{2}b{)}^3\right(-16a^2{c}^3{)}^3$ is ___

1. 6
2. 9
3. 10
4. 8

Q. The value of the product $6xy\times 12x^2{y}^2$ is same as the value of product?

1. $72x^2{y}^2$
2. $12xy\times 6xy$
3. $12x^2{y}^2\times 6xy$
4. $12x^2{y}^2\times 6x^2{y}^2$

Q.

Simplify ${(2^5÷2^8)}^5$ × $2^{-5}.$

1. $\frac{1}{2^{10}}$

2. $\frac{1}{2^{20}}$

3. $\frac{1}{2^{(-5)}}$

4. $\frac{1}{2^{(-15)}}$

Q. State True or False:
On subtracting $x^3-4x-1$ from $3x^3-x^2+6$, the answer is $2x^3-x^2+4x+7$.

1. True
2. False

Q.

Write the following in exponential form.

$3\times s\times s\times g\times g\times n\times n$

Q. Find the value of $(3^{-2}{)}^2$.

1. $2^{-4}$
2. $3^{-4}$
3. $3^0$
4. $3^2$

Q.

How do you find the square root of $-63$ ?

Q.

Question 160(iii)

For each hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.