Exponents in Fractions

Q.

Express $\frac{1}{27}$ in exponential form

1. $3^{-3}$

2. $3^3$

3. $3^4$

4. $3^{-4}$

Q.

Express $\frac{1}{81}$ in exponential form

1. $3^3$

2. $3^{-3}$

3. $3^4$

4. $3^{-4}$

Q.

The product of third power of $\frac{1}{4}$ and fourth power of 4 equals to ______.

1. 

2. 

3. 

4. 4

Q.

State whether this statement is true or false: $5^2$ + $5^3$ = $5^5$

1. True

2. False

Q.

$2^{(-4)}=\frac{1}{a}$ then a = ____, select the correct option:

1. -4

2. -16

3. 16

4. 4

Q.

Simplify:

$\frac{2\times 3^4\times 2^5}{9\times 4^2}$

Q.

Express $\frac{1}{32}$ in exponential form

1. $2^5$

2. $2^{-4}$

3. $2^4$

4. $2^{-5}$

Q. $(-6{)}^{-82}\times (81{)}^{-41}$ =
(Use exponential identities)

1. $(-36{)}^{-41}$
2. $(-486{)}^{-41}$
3. $(-54{)}^{-82}$
4. $(-87{)}^{-52}$

Q. Simplify and express the following in exponential form:
${25}^4÷5^3$

Q.

If $\frac{p}{q}={\left(\frac{2}{3}\right)}^2÷{\left(\frac{6}{7}\right)}^0$ then the value of ${\left(\frac{p}{q}\right)}^3$ is-

1. $\frac{28}{54}$

2. $\frac{54}{28}$

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

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

Q.

The exponential form of $\frac{1}{(2{)}^3}$ × $(3{)}^{-3}$ is given by which of the following expressions?

1. $6^3$

2. $6^{-3}$

3. $5^{-3}$

4. $4^{-2}$

Q.

Which one among the following is correct?

1. ${\left(\frac{a}{b}\right)}^m$ = $\frac{\left(b^m\right)}{\left(a^m\right)}$

2. ${\left(\frac{a}{b}\right)}^m$ = a

3. ${\left(\frac{a}{b}\right)}^m$ = $\frac{\left(a^m\right)}{\left(b^m\right)}$

4. ${\left(\frac{a}{b}\right)}^{-m}$ = $b^m$$a^m$

Q. Simplify and express the answer in exponential form :
$(-1{)}^{68}\times (-1{)}^{26}$

Q.

Simplify and express in exponential form:

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

Q.

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

Q.

$(-1{)}^{-3}$ is :

1. 1

2. -1

3. 0

4. 2

Q. $3^{-2}$ is equal to

1. $-3^2$
   

2. $3^2$
   
   

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

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

Q.

Find the value of $(\frac{1}{15}{)}^{-2}$ + $(\frac{1}{13}{)}^{-2}$ + $(\frac{1}{12}{)}^{-2}$.

1. 0.226

2. 41

3. 269

4. 538

Q.

$\frac{{}^{8}C_0}{6}-{}^{8}C_1+{}^{8}C_2\times 6-{}^{8}C_3\times 6^2+...{}^{8}C_8\times 6^7$ is equal to

1. $0$

2. $6^7$

3. $6^8$

4. $\frac{5^8}{6}$

Q.

${\left(\frac{5}{7}\right)}^{-5}$ is equal to :

1. ${(-\frac{5}{7})}^{-5}$

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

3. ${(-\frac{7}{5})}^5$

4. ${\left(\frac{7}{5}\right)}^5$

Q. Find out the reciprocal of ${\left(\frac{-1}{8}\right)}^6.$

Q. ${\left(\frac{x^m}{x^n}\right)}^{m+n}\times {\left(\frac{x^n}{x^l}\right)}^{n+l}\times {\left(\frac{x^l}{x^m}\right)}^{l+m}$.

Q. Find the value of m if ${\left(\frac{p}{q}\right)}^m=\frac{q^4}{p^4}$

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

1. True
2. False

Q.

Simplify $\frac{3^3\times 3^2\times 2^5}{3^4\times 2^3}$.

Q.

${\left(\frac{3}{4}\right)}^5÷{\left(\frac{3}{5}\right)}^5$ is equal to

1. ${\left(\frac{5}{4}\right)}^5$

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

3. ${\left(\frac{1}{4}\right)}^5$

4. ${\left(\frac{1}{5}\right)}^5$

Q.

The value of $(\frac{5}{2}{)}^{-2}$ is $\frac{25}{4}$.

1. True

2. False

Q.

Find the multiplicative inverse of ${10}^{-7}$.

1. ${10}^{-2}$

2. ${10}^2$

3. ${10}^7$

4. ${10}^6$

Q.

${\left(\frac{1}{5}\right)}^0$ is equal to

1. 1

2. 5

3. 0

4. $\frac{1}{5}$

Q.

Simplify :$\{\frac{1}{6^{(-2)}}-\frac{1}{3^{(-3)}}\}÷\frac{1}{5^{(-2)}}$

1. (3/5)²

2. (9/25)²

3. (5/3)²

4. (25/9)²