Negative Exponents

Q.

The value of $[4^{-1}+3^{-1}+6^{-2}{]}^{-1}$ is ___.

1. $\frac{36}{22}$

2. $\frac{38}{22}$

3. $\frac{36}{20}$

4. $\frac{36}{11}$

Q. If $m=-2$ and $n=-4$, then the value of $m^m+n^{-3}$ is ___.

1. 15
2. $\frac{15}{64}$
3. $\frac{17}{64}$
4. $-\frac{15}{64}$

Q. Find the value of $\frac{16\times 2^{n+1}-4\times 2^n}{16\times 2^{n+2}-2\times 2^{n+2}}.$

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

Q. Which one of the following options is the multiplicative inverse of $2^5$?

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

Q. What is the multiplicative inverse of $\frac{1}{4^3}$?

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

Q. Match the following expressions with their correct results using law of exponents:

1. $5^3$
2. $2^3$
3. $3^2$

Q. Find the value of $m$ for which $4^{m+2}÷4^2=4^8$

1. $8$
2. $3$
3. $2$
4. $1$

Q. Question 84
The reciprocal of $x^{-1}$ is $\frac{1}{x}$

Q. Select the equivalent expression to the following expression:
${10}^9\times {10}^{-6}$

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

Q. 1 micron equals to $\frac{1}{1000000}$ of a metre and can be written as ___.

1. ${10}^{-6}$ m
2. ${10}^{-5}$ m
3. ${10}^5$ m
4. ${10}^6$ m

Q. Match the following expressions with their correct results using law of exponents:

1. $5^3$
2. $2^3$
3. $3^2$

Q.

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

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

2. ${10}^2$

3. ${10}^7$

4. ${10}^6$

Q. Convert $1mm$ of $Hg$ into $Pa$. Take density of $Hg=13.6\times {10}^{3}kg{m}^{-3}$ and $g=9.8m{s}^{-2}$. Let it be $x$ $Pa$. Find [$\frac{x}{40}$].{where , [] is step function}

1. $3$
2. $4$
3. $6$
4. $5$

Q. Identify the greatest number among the given options.

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

Q. Relation between $m_1$ and $m_2$: $-4m_1-4m_2=3m_1-6m_2$

Q.

$4^{-2}+4^{-1}+4^0+4^2$ = ___.

1. $\frac{277}{16}$

2. $\frac{277}{18}$

3. $\frac{257}{16}$
4. $\frac{271}{18}$

Q. ${[{\left(\frac{4}{3}\right)}^{-2}-{\left(\frac{3}{4}\right)}^2]}^2=?$

1. 1
2. $\frac{1024}{81}$
3. $\frac{81}{1024}$
4. 0

Q.

What is the value of -5 raised to the power of 2?

1. 16

2. -25

3. 5

4. 25

Q. Which of the following options are equal to $3^{-2}$?

1. $\frac{1}{3^2}$
2. $\frac{1}{9}$
3. $\frac{1}{6}$
4. $9^{-1}$

Q.

Which one among the following is correct?

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

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

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

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